Sounds good for symmetric crypto, but not for public key exchanges, which is what quantum compute attacks are so far all about.

There could be double-tree PKI, where nodes in the tree are represented by two key pairs in different kinds of key spaces, with the different signatures terminating in two ephemeral key pairs, which are then used for key derivation, and the subsequent secret perhaps concatenated and boosted into a higher key space? The complexity would be mind boggling. And, weaknesses in one half of the tree could translate into a security reduction on the final symmetric key, so it would have to be way over powered to be effective.

Not a simple problem to solve.

Why wouldn't that work? Exchange all n keys with their respective methods in parallel?