That is, I don't think we disagree about what my brain is doing, merely what words to assign to what my brain is doing.

We agree on what our brains are doing. I think we disagree on whether or not our beliefs are limited to what our brains are or were doing: I suppose I'm saying that I should be said to believe right now what my brain would predictably do (belief/inference wise) on the basis of what it's doing and has already done (excluding any new information).

Suppose we divide my beliefs (on my view of 'belief') into my occurrent beliefs (stuff my brain has done or is doing) from my extrapolated beliefs (stuff it would predictably do excluding new information). If you grant that my extrapolated beliefs have some special status that differentiates them from, say, the beliefs I'll have about the episodes of The Americans I haven't watched yet, then we're debating semantics. If you don't think my extrapolated beliefs are importantly different from any old beliefs I'll have later on, then I think we're arguing about something substantial.

Nor would I say that I was explicitly aware that it followed from "car > 100kg" that "car > 12.141341 kg" prior to explicitly thinking about it.

I mean that supposing you're explicitly aware of a more general claim, say 'the car weighs more than any specific real number of kilograms less than 100kg', then you believe the (infinite) set of implied beliefs about the relation of the car's weight to every real number of kg below 100, even though your brain hasn't, and couldn't, run through all of those beliefs explicitly.