I don't have an answer for you here, alas. I'm not sure whether the built-in Apache is dynamically linked to the system OpenSSL or has its own statically linked OpenSSL (which is what we generally recommend). If it's the latter, it's obvious that upgrading OpenSSL on the system as a whole will have no effect.
I can see three options for you here:
continue to investigate the built-in Apache — If you want to do this I recommend you post your question to Apple Support Communities, run by AppleCare, where it'll reach a bigger audience whose more familiar with user-level issues.
try OS X Server — Apache isn't really part of the OS X client product, in that it's not used by any user-facing feature. OTOH, Apache is part of OS X Server, and thus I'd be very disappointed if it didn't support TLS 1.2 out of the box.
built your own Apache
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Quinn "The Eskimo!"
Apple Developer Relations, Developer Technical Support, Core OS/Hardware
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