A cheap source for these might be passive reflectors for vehicular use; often sold with double sided sticky tape on the back. A red one might be spectrally close enough to the laser's frequency so as to not attenuate it too much.

As for differentiating between the two (X vs. Y) sensors: rather than barcodes, have a single reflector for one axis, and, for the other axis, a pair of them, horizontally separated by some amount of absorptive material - a very crude barcode. It should be easy enough to differentiate between the single and double pulses, so as to know which axis is which.

Since these reflectors may not work well across a full 180 degrees, it may instead be necessary to construct convex polygons that carry multiple reflectors, so that a given reflector only has to work well across a fraction of this angular span.