The salvage titled Civic has run its course.
I have a hard enough time justifying the money to turbocharge my DC4... so I can relate to your predicament.
If the B18C1 from the Civic is in good condition, swap it to a 94-97 DC4, get it BAR'd and continue with your build.
That way, you get a clean title DC Integra for a decent price and don't lose out on the potential of the B18C1 when built.
My 2.7¥.

h: