I fished the Carolina rig a lot last year, and caught a lot of fish on it.  I also missed several, or lost them before I could get them in. 

 

My favorite thing to throw is a Zoom Z-craw on a 4/0 Gamakatsu EWG. 

 

I throw it mostly on 16lb fluoro. 

 

I felt like I had to absolutely hammer the fish when I set the hook. I'm wondering if there's a better hook option.  Should I consider a straight shank hook?

It likely isn't your hook choice, but your hook-set.  Depending on your leader length, there is a lot of line behind that sinker and a normal, quick upward hook set can only move so much line. Try reeling up all the slack while pointing your rod tip at the bait. When you feel the weight, continue reeling and sweep your rod to the side (the same way you sweep the rod when moving the bait, but quicker). That will take all of the slack out of your leader and allow for good hook penetration.

I prefer 3/0  Octopus Circle Hook. No "hook set" required!

 

https://www.tacklewarehouse.com/Gamakatsu_Octopus_Circle_Hook_Offset_Point/descpage-GOHOP.html

What papajoe222 said is exactly what I do plus I use offset round bend worm hooks.  I rarely miss or loose a fish on the Carolina rig.