I have never seen alchemist, tinker, pirate or mushroom items drop from enemies when slain by pets. So I wonder if there is a way to get that to happen? Atleast for Mushroom summon, because the rest can within the skilltree find a way to kill stuff. Or make Sporification and similar a post combat skill, like Corpse Drinking. I might just be unlucky.
The pets procs are not currently working. I'm not even sure that they are supposed to work but I think they are supposed to. I believe the devs are aware of the situation. As for a skill/spell that uses corpses, there are a few different ones and some modders may have made some or will make some in the future. Or you could always make one that does exactly what you want. Have fun.
It's a tad unfortunate to have a skill that negate almost the entire skill tree, denying one reaping the reward from kills.