I know next to nothing about this subject, but this suggestion sounds like the kinds of things that amateurs suggest but experts scoff at. So my question to any actual experts: is this legit? Note that breaking A+B is not necessarily as hard as breaking both A and B, but it certainly seems likely to be true most of the time.
I'm far from an expert, but I believe the big worry with layering systems like this is you double the amount of key management and implementation attack surface (which is often the weakest part of a cryptosystem), and traditionally it's not for much benefit.
Ignoring quantum computing, doubling up algorithms doesn't really protect you against unknown unknowns all that much as there is a good chance that a massive flaw in one of them could apply to the others (since they are all somewhat based on the same "problem").
When you start layering lattice based crypto with traditional crypto the payoff might change and make it more viable.
