I'll throw in my 2 cents just like the others.
I vote for option 3 or option 4 (i will explain) if your going to be doing a break down. Reason being, the issues you are having.
I would highly recommend you decide how much your going to throw at a 2H to get it ported, polished and rebuilt. You have to assume that the block needs to be redone if your going to go through all of this trouble to re-piston and everything. If I was going to be done this I would highly recommend getting the block looked over before you just chuck pistons in. I am assuming you are smart enough to do that.
ARP studs all the way
Gturbo all the way, you have a few options depending on your goals and boost levels. I am assuming 20-24lbs so a grunter 1 or 2 would probably have you covered.
A full proper rebuild, port and polish and all that jazz I would estimate to be around 4-5k. That is my guess, don't flame me if I am right off. But I know a full turbo piston set for a 1hz along with a rebuild kit is upwards of 2k + in Australia. Its gotta be similar with the 2H
Option 4:
I see this option being fun but expensive enough in the end to have an inferior engine in terms of performance to a 1hd-t. You could chuck in a 12h-t but you are then facing a dated engine and harder to find parts down the road. I think your good about 20lbs of boost with a gturbo on one.
Throw in a 1hd-t and a gturbo, custom plenum and a big airbox and you will be off to the races. Youll need to track down a performance clutch and a 1hz bell housing and change your input shaft on your h55f. Since you have to do that break down throw in a macnamara gear into your transfer to prolong your output shaft of your h55f and your golden.
either way you have to decide what your goals are with the truck, how long you plan on keeping it and what your budget it.