H22 swap issues, please help!!!

Ok, first off let me state I am not a DIYer when it comes to motor swaps. I actually have this swap done at a shop. I had a 99 base model prelude that I loved to death and totaled. Pulled everything out to put into a 2000 ex coupe that I purchased for $1500 with the stock f23 block and no head. At first I was going to put the h22 head onto the the f23 block but the shop told me it would be cheaper to just drop the entire h22 in there. So after 3 months of them struggling to do it (which to me was odd because they do hondas often and this swap doesnt seem to difficult or uncommon) they are telling me that there is play in the crank of my block.
I had them rebuild the head, the block has a little under 160k on it. I had skunk2 pro1 cams installed, supertech valve train, aem cam gears, skunk2 66mm thorttle body port matched to a modified h22 intake mani, i actually purchased a skunk2 intake mani cause this build was originally intended for my prelude.
They are telling me the only true way to address the issue is to rebuild the block and micro polish the crank. The downside is it would add about $2,000 to an already $6,000 build (parts, labor, I also had some extra stuff done like fog lights, HIDs, etc) and another 2-3 weeks time. The plus side is it would be a fresh new motor basically. They suggested just driving with play in the crank...
I eventually want to rebuild the block. My question for the forum is (sorry it took so long to get to and sorry if the answer is posted already as I am sure it is) should I rebuild the h22 block or should I rebuild the f23 block that came with the car? Any benefits to h22 vs g23? I am leaning more towards f23 because I can drive my car with the h22 while they build that block, and also its better for boost which I will be doing come income tax time.
My second question which are the best forged pistons for my f23 block? Do I need a particular kind if this block is going with an h22a4 head? does that even mean anything? Can I only use f23 specific aftermarket pistons? Can I use k or h series and are they better than aftermarket?
Any help/advice greatly appreciated. My car is ready, I am just waiting for an exhaust in the mail before they dyno it. They say it should easily be at 200whp...

Wish I could help but good luck. Sounds like a great build

Thing about a G23 motor you can't rev as high as the H22, due to the bearings in the crank because its a low compression bottom end thus limiting it....they were not intend to rev to 7200rpm....if you want to do an G23 I believe you'd have to have custom upgrade your bearings to handle such abuse......that might cost more then what's out in the market, not sure.........also you have to cut and weld between f and h water pipe, weld two oil passages on your h22 cylinder head and swap the crank sprocket and waterpump gears.......yeah this swap is cheaper but can't say its very reliable if the bearing are not upgraded to handle the high rev like I mention before revving pass 6500rpm might be risky to the motor health.Since you already have an h motor I build that and rebalancing the crank would be more beneficial if what they claim to be true.....you can also find by asking the shop that will rebalance it to see if its balance is off, but of course that's forking out more money.....but if youre going all out might as well get it rebalance might save you trouble later down the line. As for the F23 you can always find another one for cheap at the junkyards or even buy a low mileage from an jdm shop. And these motors are better for boost........even as a stock motor it can handle 10psi with a properly tuned ecu......sorry if my for any grammatical error typeds this through my phone

The h22 is a good motor. But for boost it will need to be sleeved. If you do g23, it's great for boost. Iron walls, dual over head cam. There isn't a problem with the revving and because it's still a f23 bottom, you'll see revs closer resembling a f23. You can get forged pistons simple, rods requires a little more researching but should still be easy to find. Also, with a g23 you could bore it out 1 over to 87mm while you're at it. I have heard that that could be risky so doing .5 or nothing over is probably the better option. The g23 swap has been discussed to death on this forum and pretty much any answer you want can be found here.