Then it seems like speedlites would be a better option to freeze the drops completely, since they don't have the tail burn that those strobes have
At full discharge, Speedlights have the same illumination decay as any xenon flash and the t0.1 rating is middling. At lower energy settings, the output curve is indeed chopped by IGBT but studio packs (whether IGBT or bank-switched) can deliver the same luminous energy at respectively lower energy settings where t0.1 can be 1/10,000s or shorter. A short t0.1 will freeze the raindrops entirely. For example, the Profoto Pro-10 in freeze mode at setting "5" will discharge 75J in 1/20,000s t0.5 IGBT. 75J is a full-energy discharge for a big Speedlight.
Of course, Bart may not want frozen raindrops.