One of the 5e splatbooks included improved reagent variants that can be consumed to reduce drain by a flat amount per reagent used. So as long as you're stocked on those you basically get to fire off miniature nukes as much as you like, and shifters get innate bonus initiative for the potential for IIRC 3+ action passes per turn. IIRC the math works out to something like 2000 nuyen per force 14 (assuming you took exceptional attribute: magic and a 7 in magic at chargen) fireball to completely negate the drain, which IIRC is about on par with what a dumbfired rocket costs (guided missiles being more expensive) but without being outright illegal or requiring heavy barter checks to acquire. In fact, I think I built a character based around exploiting exactly that combo, though I never played it. A mystic adept with improved reflexes can accomplish functionally the same thing too.

Otherwise you're right that regeneration doesn't help with drain, though I can't remember if it's rolled or a flat recovery amount per turn in 5e.