I don't think you can ever have enough life on hit. I went from 300 to 1k and it made a huge difference. Attack speed is obviously going to help take advantage of LOH but it isn't 100% necessary imo.
Here are my A3i stats right now:
It's kind of hit or miss at the moment. I'm still having trouble tanking full champion packs. I can usually 1v1 any combo but handling 3v1 requires a lot of kiting. 14k DPS is probably too low but I had to make sacrifices to increase my health pool. Most of my equipment is pretty awful overall. I still need to upgrade most of my pieces (helm, bracers, and belt need major replacements)
I'll probably pick up a better LOH weapon once prices drop a little to go to 1500-1800 LOH which should help me with things like plague/molten/desecrator. If you're in the position to get to 20k dps it wouldn't hurt either. I have a ring and belt that I switch out to go from 14k to 18k and it helps a lot when dealing with white mobs.
Also remember to buff your followers. I got my enchantress up to 5k damage and it makes things a lot easier.