didnt bother reading the whole story, but here i go..
the F22 is 2.2 litres because of the bore diameter of 85mm. the H23 does share the same crank and rods as the F22, but the 87mm bore of the H23 is what gives it the 2.3 litre displacement.
putting H22 rods and pistons on an H23 crank will result in TDC being a few millimetres above the block's deck, therefore severly increasing compression to the point of not operating. the only internals that swap between the H22 and H23 are the pistons. you can put the H22 pistons into the H23's block with H23 rods and crank... combined with the H22 head, you'll get 10.1:1 compression. if you use a whole H23 block with VTEC head, you'll get 9.3:1 compression since the H22's head has larger volume combustion chambers (approx +3.8cc) than the H23 head.
the F22's rotating assembly is identical to the H23's assembly... it's where Honda used shelf parts to make a different motor.
some measurements you'll need:
H23A1 stock compression: 9.8:1
H22A4 stock compression: 10.1:1
H23A1 block piston bore: 87mm
H23A1 block stroke length: 95mm
H23A1 rod length: 141.5mm
H23A1 rod/stroke ratio: 1.49:1
H22A4 block piston bore: 87mm
H22A4 block stroke length: 90mm
H22A4 rod length: 143.0mm
H22A4 rod/stroke ratio: 1.59:1
H23A1 head chamber volume: 50.0cc
H22A4 head chamber volume: 53.8cc
H23A1 stock piston displacement: -5.1cc
H22A4 stock piston displacement: 1.3cc
H22A4 head with H23A1 block: 9.3:1
F22A/B block stroke length: 95mm
F22A/B block piston bore: 85mm
F22A/B rod length: 141.5mm
F22A/B features same rod and stroke as H23A1
you'll need to use the H23 dizzy you have, as the H22A4 is OBD II, and will require a rewiring of the motor harness should you go that route. using the H23A block, H23 dizzy, H22 pistons, and H22 head will provide you with 10.1:1 compression, with 2.3 litres of displacement. the H23 bottom end isnt great for revving high due to excessive lateral force from the poor rod/stroke ratio, but you should be able to gain a few more ponies over an equivalent stock H22 setup.
for simplicity sake, i assume you're going to put this setup into your Accord.
here's what you have that you'll use:
H23 block
H22 pistons
H23 dizzy
H22 head
H23 engine wiring harness
P13 ecu
H22 head gasket
H22 timing belt
H23 balancer belt
H22 timing gear
H22 water pump
the P13 ecu is the H22A1 93-95 OBD I ecu. you can use a 94-95 Accord EX ecu, but you'll lose the secondary runner function and knock sensor. 94-95 P72 GSR ecu is also capable after reprogramming the fuel map for H22/H23 duty.
the reason why i chose this parts list for you is to keep it simple and stay with OBD I. no sensor swapping or rewiring (except VTEC, since the H23 harness has no plugs) since both motor and the car are OBD I. the H23 block is also a solid deck, much more durable than the H22A4's open deck. you can swap over the H22's oil squirters into the H23, but it really isnt worth it... they require a bit of bending to fit properly.
you'll need to change everything that touches the timing belt, too. the H22 cam gears have a different amount of teeth than the H23's, so you need to get an H22 timing belt, water pump, and the timing gear off the crank, and swap those to the H23 block. as for the intake and exhaust manifolds, obviously use the H22's setup, as the H23 exhaust manifold wont bolt up to the H22 head.