13 outs on the flop sounds good.
What do you do with 13+ outs on the turn? Would you still push? Your implied odds may have reduced because you may well be all in after pushing on the turn but I would have thought that with 13 outs it still may be EV+.
I tend not to push on the flop with straight and flush draws. I like to see the turn first. If the board pairs on the turn I'm not committed to going all the way. If the board doesn't pair my outs are good. I hate going all in on the flop and see the board pair on the turn in this situation. By delaying the push I protect myself against this. I don't know if my thinking is correct in this situation FWIW.

Monk's patented top five steps to trouble-free drawing (TM)...

1) There's outs and there's outs. I'm not keen on considering the strength of a draw just on the number of outs, nut or otherwise. On a board of Jc Tc 2d, KQ offsuited has 8 outs (or rather, 6 nut outs) but even then it's probably not worth that much - even if you catch your draw on the turn you still have as many as 25 cards to dodge on the river. Outs to a boat are always stronger than outs to a flush, which are stronger than outs to a straight, due to the redraw possibilities. A set vs a made straight has higher equity as a drawing hand than a 9-outer straight draw vs a set, even though the straight draw has more outs the boat draw will always be good every time it hits, and can't be redrawn.

Mind you, as the "strength" of the various draws increases, in general the implied odds decrease as the draw is more obvious. A flush draw is great but you often won't get paid if it shows as it's quite obvious. Straight draws, especially odd or low ones, often have great implied odds as people don't assume they are very likely. If the board shows K[s] 4[s] 2[c] and you have 35, it might be worth calling some opponents even if you don't have a flush draw; although you only have 6 nut outs, many opponents will assume you're drawing to a flush and put in another pot bet if 6 or an A appears.... You'll get paid on this hand much better than you will if you draw to the less vulnerable (but more obvious) nut flush.

In omaha, the stronger draws often have less implied odds. Remember a) not all outs are created equal and straight outs in particular can face massive redraws on the river and b) hidden or apparently unusual draws, which your opponents will not give you credit for, have great implied odds and holding one often makes calling a reasonable play even if the strength of the draw is weaker than you'd like.

2) Non-nut outs can be as good as nut outs if you have a good read. If your opponent re-raises on a board with no flush or straight showing, he probably has a set, and therefore if you have 4 outs to a non-nut straight at the bottom end it's probably going to be good. However, you can discount those bottom end straight outs if two more callers come along for the ride as they probably have straight draws that will make higher straights to those outs.

3) Consider players left to act. They're not ALWAYS bad for a drawing player - if you're OOP to a maniac who raises every flop, then you have to be worried about it, equally if there's the possibility of a strong made hand on the board (a straight for instance), and 6 players left to act, you may wish to view your nut flush draw with some caution as the chances of someone raising after you (devaluing your draw) are good. Equally, you have to view non-nut outs with more suspicion if there's players left to act - if you're closing the betting and there's been one better and no callers, your non-nut outs are more likely good. Drawing to a K-high flush when there's 5 players still to act is not smart as one of them could easily have the A-high draw and you could be unknowingly drawing to secon best.

However, players left to act CAN be a positive thing for draws in some cases. If the table is passive, and there are maybe a few possible draws on board, a hand like the nut flush draw may have better odds to call a bet in early position due to the likelihood of someone else calling along the way - the more players who call, the more seem to put money in, dragging it into the pot like a magnet. If the table is sufficiently passive, and the board contains no made straights or flushes (i.e. the only likely raiser would be a set or an over-aggressive player), you may wish to use this as a valuable reason to call a draw that would be -EV.

Having players left to act who might call is only a good thing if your draw is one to which extra bets comprise dead money. If you have a flush draw, or top set with a flush or straight on the board, your hand cannot be beaten by any other draws, if you don't make your draw you'll lose to the made hand but if your draw makes, the other player calling bets is merely escalating the size of your pot, rather than playing to a hand that can hurt you. This is the case if you hold a nut flush draw, call a bet by a player who has a set, and a second player with a straight draw calls after you - the guy with a straight draw is totally dead money to your hand. He can still win the pot but only if the flush doesn't come; if that happens you'd have lost to the set anyhow.

Whether the players left to act represent a strengthening or weakening of a drawing hand is a judgement call, but it's something that comes with experience and something you need to consider very strongly when putting in reasonable amounts of money with a draw.

4) Sometimes you have fold equity to draw, and this can improve the strength of your draw. This is usually only the case when heads up, and against a player with a made (but presumably vulnerable) hand who knows how to fold. If you hold a flush draw when there's a straight on the board, you may wish to take a punt at calling an opponent you suspect has the made straight, with the possibility that you might be able to bluff and represent a full house if the board pairs. In this case, you'd like to be in position; if the board pairs and he makes what appears to be a blocking bet or checks, he's just asking to have the pot taken away from him. Note that this only works against straightforward players who know how to fold. Note also there are some occasions when you're drawing in which your fold equity is better when you're out of position, though these are rare.

5) Backdoor draw give more equity than you'd often expect, especially when your opponent has no kill cards (i.e. if you can make the backdoor draw it'll always win and not lose to a flush or something made by your opponent). Although it depends a little on your draw, a backdoor draw can be worth as much as 5% of the total pot equity, and is usually worth 3% at least. A completely clean backdoor flush draw wins the pot 5% of the time. Backdoor WRAPS can be even more useful - if you're drawing to a flush draw with a hand like A[s] K[d] J[s] Th[h] and the board shows Q[s] 4[s] 2[d], the fact you have 4 wrap cards round the Q gives you a significant nnumber of backdoor draws - if you see a 9, T, J, A or K on the turn you'll gain a good 9 outs, more in some cases.

My take on the Wide World Of Draws, anyhow.

What I'm really concerned with here is setting up overlay situations along the lines of Monk's points 2 and 4.

Taking a board of Ks6h5d, let's say I bet out pot in EP. Up to now, I might do this with some kind of 66 or KK or A478 (13 outs). If I get raised, I would push KK, fold 66 (usually) and call with A478.

What I'm suggesting here is pushing rather than calling with A478. For one thing, it puts a lot of pressure on 66 or K6, who in point of fact have to fold, even though 66 is fairly significantly ahead. Also, if "they" catch you doing this, as they eventually will, it buys you callers on your own KK, to which 66 (unless it's 6678) is in a big predicament.

As to the question of what to do on the turn if you get a caller, I think it's a little flexible here. Let's say I was specifically betting Ad4d7h8h, but I'm also repping KK, and the call is more often than not some kind of draw rather than 66. OOP I'll probably bet half pot here if the board pairs on the turn, repping KK.

On other cards, they can either help or hurt your draw. If the turn comes off a diamond or a heart here, that helps my drawing hand, so I'll pot again, largely for the purpose of setting up a river bluff if the river blanks. If a spade comes that doesn't make the straight, that hurts my hand, so I'd say checking is probably not a bad idea (?). If it's a club, completing the rainbow and still giving 13 outs, then I think betting it still probably works.

What I'm mainly advocating is pushing as slight underdog in some situations largely for the purpose of setting up calls when you have an overlay.

Yes, maniac play can be profitable in PLO.