Powering 12V 35W halogen bulbs with a constant current supply
I don't generally see people dimming halogen or incandescent bulbs
with constant current devices, and there must be a reason for this.
Any ideas?

Price. It is much easier to power a bulb with a battery, mains, transformer.

Or, does the unit just modulate voltage to indirectly control current?

Correctly, almost all current sources do it that way. Practically, there is no such a device like intrinsic current source, just theoretical. But it could be true somewhere in the universe, so we're ready to use our equations.

Am I correct in thinking that this setup negates voltage drop
considerations for the bulb over a long cable?

Yes.