Um, don't say a stock R wont run 13's if you haven't run one.
I ran my friend's CX hatch, only weight reduction was the spare tire in the trunk removed.
I ran a 13.8x on MT slicks mounted on 15" slipstreams. He had basically this
99 b18c5
skunk 2 intake manifold
DC ceramic header (which I ran open header at the track)
AEM hybrid intake
ground wire kit
skunk2 knob and shifter
OBD1 P72
VAFC (version 1)
that is essentially stock with bolt ons and a VAFC.
I bet that with a chipped ECU, cams, and a quick port n polish on the head, you can get the sedan into 13's or at least 14 flat with a b18c5.
K20, yes, everyone would love to try one out in their EG, but the funds arent always there. B series is by far the most versatile of all civic motors. Anyway, you'll be happy with a c5 or even a fully built c1.
ORR you can go cheaper and buy a c5 block and a b16 head and piece together your motor. Plus, you get to choose which tranny you wanna go with as well.