Can anyone confirm for me that both effects fire correctly with a weapon that has two enchantments attached? This is very important.

I can't vouch for every combination, but in general I haven't had any problems and I use the Extra Effect quite often. Damage and Absorb enchantments work fine together as far as I can tell, they both work fine with Soul Trap, etc. I've not yet found a combination where I came to suspect that one of them wasn't working.

Gah. Currently, some of the spells in my mod aren't playing nice with weapon enchantments and I'm trying to figure out how Bethesda got around that issue to allow two weapon enchantments at once.