Can cross-polarization be achieved with two linearly polarized (flash) lamps; one either side of a circularly polarized lens?
Lens attachments tend to be circularly polarized, while the PVA sheets available online tend to be linearly polarized.
I'm trying to tame some surface reflections and I'd like to know before I get my hopes up and invest too much time & effort into trying to fit a square peg in a round hole.
Yes. Both of these filters exclude light that doesn't match the appropriate direction of polarization. Circular polarizing filters start with a linear polarization filter. They then also have a quarter-wave plate which transforms the light which has got past the filter so that it doesn't mess up autofocus and metering systems.
There's more on the background of how circular polarizers work What is the difference between a linear and a circular polarizer?, but for the purposes of this question, the basic answer is don't worry about it.