If you have good poultry shears, you should try "spatchcock" method -- cut the spine out and spread it out meat-up. The body cavity wall takes the brunt of the direct heat.

Nowadays I do that with all of the whole birds. Thanksgiving around here is a hoot; two 16-ish pound birds in the grill billows out some serious fog (smoke) and the whole 'hood smells *so* good!