Since numbers are aphysical, how do we relate this to causal relations?

You just begged the question. Eliezer answered you in the OP:

Because you can prove once and for all that in any process which behaves like integers, 2 thingies + 2 thingies = 4 thingies. You can store this general fact, and recall the resulting prediction, for many different places inside reality where physical things behave in accordance with the number-axioms. Moreover, so long as we believe that a calculator behaves like numbers, pressing '2 + 2' on a calculator and getting '4' tells us that 2 + 2 = 4 is true of numbers and then to expect four apples in the bowl. It's not like anything fundamentally different from that is going on when we try to add 2 + 2 inside our own brains - all the information we get about these 'logical models' is coming from the observation of physical things that allegedly behave like their axioms, whether it's our neurally-patterned thought processes, or a calculator, or apples in a bowl.

I can't think of an example, but I'm thinking that if a property existed then it would be a causal relation. A property wouldn't represent a causal relation, it would be one. I wasn't thinking mathematically but instead in terms of a more commonplace understanding of properties as things like red and yellow and blue.

The argument made by the simple idea of truth might be a way to get us from physical states (which are causal relations) to numbers. If you believe that counting sheep is a valid operation, then quantifying color also seems fine. The reason I spoke in terms of causal relations is because I believe understanding qualities as causal relations between things allows us to deduce properties about things through a combination of Salmonoff Induction and the method described in this post.

Are you questioning the idea that numbers or properties are a quality about objects? If so, what are they?

I'm feeling confused though. If the definition of property used here doesn't connect to or means something completely different than facts about objects, then I'm way off base. I might also be off base for other reasons. Not sure.