I just used a router and a board clamped down as an edge guide.
Sorry for the late reply. I don’t remember getting a notification about these posts…
You can use any caulk but this is the acoustic caulk I used… Franklin International 2892 Sound Sealant, 28-Ounce, Green https://www.amazon.com/dp/B00171JEC6/ref=cm_sw_r_cp_apa_i_sgpcCbQ0Z1V61.
Just make a test rabbet joint a a scrap piece of acrylic to test the perfect depth. I think 1/16" extra for the caulk will probably get you very close.