There is a cap on how fast IC can be paid for.  Does a similar cap exist for BP construction, if I am so inclined?

Not that I am aware of.
There is the scaling cost, so each additional costs more.
That cost is calculated in the Infrastructure Expenditures/BP Construction/"Total needed" field.
However BP can only be built in the homeland.

It is my expectation that since we boosted Colony development speed and receipts, that we will get to a place where
folks feel like they have extra $, and at that point warship Reconstruction, and BP construction will occur.