Security of Diffie-Hellman when one party has a flawed RNG (compared to TOFU)
There are a few things missing from this question.

First of all, TOFU (trust-on-first-use) is not a scheme and cannot therefore be compared with DH. TOFU is more a property of a protocol than anything else. 

Second, you say you would use "some kind of authentication". This is what TOFU "solves", establishing trust without which it is impossible to authenticate. You cannot just skip over that part of the protocol if you want to compare schemes.

Third, I don't see any  comparison between active attacks and passive attacks. If an attacker can create the private key then passive (eavesdropping) attacks would be possible. It is not clear if passive attacks are possible for TOFU as it is not a protocol or scheme in itself. That said, I think it is tricky to think of a scheme where a broken RNG isn't an issue in itself.

Finally, for your own scheme you say that you "generate random nonces" but it is unclear how these nonces are shared or what they would add if they would be shared publicly.