hostile mob sorter

hey there!! so i've been trying to figure out how to make a mob sorter for my mob farm. so maybe this post will help someone build their own! though there are still some troubles so help would be really appreciated

so here's the part where mobs come through. instead of this big platform with dispensers with spawn eggs there will be a farm

mobs go through a 2-block wide tunnel at first, which isn't really convenient, so here they drop into a 1-block wide tunnel.

here baby zombies get sorted out

 then there's the undead sorter. undead mobs (zombies and skeletons) can't swim, so they sink to the bottom. witches and creepers float to the top.

here zombies and skeletons get separated. couldn't figure out hoe to use water for this :( so i used redstone. when a mob passes the observer with a string, it sends a signal to the pistons, delayed by repeaters. mobs fall on the lily pad on a waterlogged trapdoor. the tunnel where zombies go has a lantern overhead. that creates a gap exactly the height of a zombie, so they can get through but skeletons can't. skeletons then get pushed by the second piston into their own tunnel.

another angle

 here witches get separated from creepers. and THAT'S where troubles appear. they all get stuck and I don't know what to do about it

also this sorter isn't compatible with spiders. if you know how to fix this, please let me know!!!!