Constructing a formal specification from RFC8446 is possible.
Constructing a formal specification for PKIX... is not. PKIX is specified by a large number of RFCs and ITU-T/ISO specs, some of which are more formal than others. E.g., constructing a formal specification for ASN.1 should be possible (though a lot of work), while constructing a formal specification for certificate validation is really hard, especially if you must support complex PKIs like DoD's. Checking CRLs and OCSP, among other things, requires support for HTTP, and even LDAP, so now you have... a bunch more RFCs to construct formal descriptions of.
And there had better be no bugs in the formal descriptions you construct from all these specs! Recall, they're mostly not formal specs at all -- they're written in English, with smatterings of ASN.1 (which is formal, though the specs for it, though they're very very good, mostly aren't formal).
The CVE in question is in the PKIX part of OpenSSL, not the TLS implementation.
What you're asking for is not 5 man-years worth of work, but tens of man-decades. The number of people with deep knowledge of all this stuff is minute as it is -- maybe just a handful, tens at most. The number of people with deep knowledge of a lot of this stuff is larger, but still minute. So you're asking to spend decades' worth of a tiny band of people's time on this project, when there are other valuable things for them to do.
The number of people who can do dev work in this space is much larger, of course -- in the thousands. But very few of them have the right expertise to work on a formal, verified implementation of PKIX.
Plus, it's all a moving target.
Sure, we could... train a lot of people just for such a project, but it takes time to do that, and it still takes time from that tiny band of people who know this stuff really well.
I'm afraid you're asking for unobtanium.
EDIT: Plus, there's probably tens of millions of current dollars' (if not more) worth of development embodied in OpenSSL as it stands. It's probably at least that much to replace it with a verified implementation, and probably much more because the value of programmers expert enough to do it is much more than the $200K/year suggested above (even if you train new ones, it would take years of training, and then they would be just as valuable). I think a proper , formally verified replacement of OpenSSL would probably run into the hundreds of millions, especially if it's one huge project since those tend to fail.