Zero-mod-p was an IPSEC fault, as was subgroup negotiation (but you mentioned NIST groups earlier).

Lots of people have done their own implementations of DH (DH is trivial to implement; it's just a couple lines of Ruby); how many of them do you think caught these flaws?

I have no idea what the utility of the public key is in the system you just described. Public key crypto adds susceptibility to attack; it doesn't ever really spare you from it. Here, you're vulnerable both to attacks on your HMAC verification and to implementation flaws in your more number-theoretic (and way more dangerous) public key code.