You can't multiply two amplitudes together.
You do this whenever you calculate the amplitude contributed by a single history within a sum over histories. The amplitude for an event is exp(i.action) and action is additive, so the amplitude for two events forming a single history is the product of their individual amplitudes, exp(i.action1+i.action2). In this respect it's just like ordinary probability theory, where you multiply probabilities for conjunction of events and add them for disjunction.
I don't understand the motivation or the assumptions for what you are doing. Quantum cosmology is such a guessing game that even unusual formal generalizations might lead somewhere, and I would like to offer you useful feedback, but I'm wondering if there's some basic misconception about QM motivating you.
the amplitude for two events forming a single history is the product of their individual amplitudes
I'm not sure I understand. What is an "event"?
I've noticed that the amplitude of a system is equal to the product of the amplitudes of the component particles, but that's just mathematical shorthand. Individual particles don't have their own amplitude. Only the universe does.
I don't understand the motivation or the assumptions for what you are doing.
I'm trying to make it simpler. It's not much, but each bit you can shave off of the equations doubles the probability.
Timeless physics is what you end up with if you take MWI, assume the universe is a standing wave, and remove the extraneous variables. From what I understand, for the most part you can take a standing wave and add a time-reversed version, you end up with a standing wave that only uses real numbers. The problem with this is that the universe isn't quite time symmetric.
If I ignore that complex numbers ever were used in quantum physics, it seems unlikely that complex numbers is the correct solution. Is there another one? Should I be reversing charge and parity as well as time when I make the standing real-only wave?