I'll chime in on this since I have done a few bodies.
- I use the double stick tape from Woodcraft, and it is almost too strong. I have started using screws just because it is easier to get the template off
- My templates are MDF as well, but I don't really like working with the stuff. It is nasty. I haven't found a good alternative yet.
- I have never used my router with anything lower than full speed
- I do almost all of my perimeter routing with a router table
- I use both a top and bottom bearing bit when I rout. I use the top bearing bit with the template first, then take the template off and use the just routed section as a template with the same bit, then flip the body over and use a bottom bearing bit to get the rest of the material. Always use good sharp bits and you shouldn't have a problem with tearout/burning.
Also, take off as much extra wood as you can before you rout. I mean all of it, I like to take the amount of excess around the template down to the thickness of the pencil line I used to mark the wood.