I'm using an 8" JA Henckels chef knife to slice the bark. Using heat gloves, it feels really small and slippery in my hands. I have smaller hands & I don't want to bust the piggy bank.... I appreciate it.
Why would you need to hold the knife with a heat glove?
A traditional meat cleaver is intended for heavy duty meat prep which would be unusual for a home cook.
I have a Chinese cleaver (I rarely use) which is much lighter than a meat cleaver and intended for lighter duty like veggies.
Maybe there is an alternative to accomplish what you are trying to do.
Slicing large cuts of meat is more effective with a Slicer. Do you mean chopping bark? Brisket? Pork?
Maybe your current knife is dull.