After having the router tear out on me time and time again regardless of what I tried to alleviate the issue, I've given up on that method.
Now I use my template to draw the line on the body, then I set the template aside. From there I just bandsaw extremely close to the line and then sand up to the line on the oscillating spindle sander simply using my eye. No tear-out, and the body edges are nice and smooth.
It took a little practice to develop the skill so that my curves were smooth without flat spots. The trick is to always keep the piece moving and not take too much off at a time and just sneak up on your line. Once I got good at this method it takes me no more time than setting up the router. The lack of worry about the router bit grabbing hours worth of work and tossing chunks of it across the room was worth the time invested in honing my ability. As a bonus, it's more fun than routing. Gives me kind of the same feeling as carving a neck.
Is it as precise as a router/template method? No. Is it close enough that the differences can't be seen by eye? Yes.
That's the general approach I use too, for body perimeters. I build my bodies as a top and a back, of equal thickness (0.700" on most of my models). Before cutting out the perimeter on the top and back, I do all the internal routing of cavities and chambers. This is done with routing templates that fit into reference holes on the inside surfaces of the blanks.
When the internal chambers are done, I use my Master template to draw a pencil line of the perimeter on the top and back. The Master template also pins into the same reference holes. Then I bandsaw out the perimeter on the top and back, cutting real close to the pencil lines. Next, I glue the top and back together, using permanent (plastic) dowels in the reference holes to line them up. The perimeters are a pretty close match, within 1/16". I finish up the external pocket routing; neck pocket, control cavity cleanout, etc.
I finish up the perimeter as the final step in making the body. All the other stuff needs to be located accurately, but the perimeter doesn't need to be precise dimensionally. It just needs to look good. I clean up the perimeter on the spindle sander and the end roller of my edge sander, and then work it in the vise with hand sanding blocks. It's still a squared edge, but it's important to get the shape smooth and
fair (a boatbuilding term). You shouldn't be able to see or feel any lumps or discontinuities in the perimeter shape.
Then I go over it with the router and a big roundover bit, from the top and the back, to get the radiused edges I want. It's a bearing bit, with the bearing following right on the glue line. That's why the perimeter needs to be
fair, so the radiuses will also be
fair. To avoid tearout, I go around in several steps of depth of the bit. The last pass goes in the climb direction, and only takes off about 1/64".
Using that sequence, the final perimeter is usually pretty good, requiring only a little bit of light sanding with a rubber block.