Do you have a slow cooker or pressure cooker? If not, they are a good investment for hot summer month cooking.
You might also consider the microwave. You could par cook the veggies in separate customized batches in the microwave and then finish them off on the grill to add that caramelized flavor. That's how I do caramelized onions so it doesn't take so long for them to carmelize on the stove.
You might also be able to put them in some hobo/foil packs and do them on the grill. It will trap the steam to help them cook while getting some browning from the heat.