your HU theories are right on the money.
it is very awkward to switch styles of heads-up, but it shouldn't be too hard to adjust. just play the way you normally do when it is folded to you in the SB.

as for the hands, hand 1 is an obvious trap unless villain has a history of not keeping the initiative heads-up. check the flop, fold UI whenever he gets around to betting.

hand 2 raise preflop.