Suggestion?
I do differently.
Take the veggie, cut it the way you want it - salt and lay it out for awhile. The salt will cause juice to rise to the surface.
Just before you cook, wipe off the juice.
Now the veggie wants fluids.
Throw the veggie on the grill, with the tough (the skin or back) side down. Brush the veggie with a bbq sauce - if you want an easy sauce, just use 1/2 olive oil, and 1/2 balsamic vinegar or lime/orange juice - and then season like you want it. Add a little honey to make it stick. Not much.
BBQ sauce, as we use it, is thicker than marinades. So it sticks to the outside, and the result is yummy!