Well, I play a lot of HU tournament style but none cash style. This is in any case what I'd do:

I'd cut WAY back on the raises. I usually raise something like 30% or so, and I'd probably cut that back against someone who calls 70% of the time. I go up to raising any ds if they're folding a lot. If they're calling a lot, I raise only big hands (wraps and big pairs basically).

Also sounds like he's stabbing too much on the turn. I'd check-raise some decent hands to him. Pretty good is whenever you check some little pair, then spike 2 pair or trips on the turn.

It really sounds like he's kind of station-ish passive. So, in general, I like to play pretty straightforward against that kind of player, trying more to chip away in medium-sized pots (hence also less frequent with the raises).

As long as he's check-calling a lot, I just wouldn't bet without a hand (which for me includes TP, open-ender, any flush draw as well as truly strong hands).

I'm not at all sure whether this is optimal, but that's usually what I do, and it seems to work alright.

What do you have in mind? Play a certain number of hands? Or play until one player loses a certain number of buyins? I'm happy to organize something but I'm not sure what is the best format.