Especially at 350 mA (if that's led current), I'd say being able to use lithiums is an absolute requirement. i hope you'll do whatever it takes to set up the electronics to ensure proper operations with lithiums.
I think I'd want 200 mA, since I want the light to be at least somewhat useful with the cheap zinc-carbon batteries that are occasionally all one can find in a pinch. I think 350 mA would wipe out those batteries almost instantly, while 200 mA would last a useful period. Also, 350 mA might run pretty hot, in such a small light.