Since both the 3750-E and 3750 are multilayer switches, you could route on either, although if you route on the IDF stacks, you'll likely want to stop spanning VLANs across multiple IDFs.

Normally if you enable routing on your MDF stack, you would use a dynamic routing protocol between it and your core routers (although I would select a better oriented IGP rather than iBGP). Or, you can enable routing on the MDF, use a couple of default static routes to MSRP addresses on the 6500s and then make the MDF the HSRP gateway.