The deck looks solid. One thing I could recommend atm is putting a greater emphasis on creatures with Hexproof. Being able to assemble a Hexproof and Indestructible commander (or board) feels like one of the biggest payoffs for Kathril.
Carnage Tyrant is a good means to that end, as it comes with Trample and a decent body if you need it.
Otherwise, playing cards like
Ephemerate and Yannik to spread the Kathril buffs around without needing it to die could be nice. Depends on whether you're interested in that, or just buffing up Kathril.
Throwing more good cards in wouldn't hurt either.
Entomb,
Victimize,
Lightning Greaves, and
Dread Return all seem like they'd be good if you can fit them.
Dread Return might be the least applicable, since you don't seem to swarm the field with bodies. I just like it in theory because it makes your "tutor to graveyard" effects a little more flexible.