When I went with a TP design tub I researched this topic until I was cross-eyed.
Few pointers from my limited experience:
1. How good is your cover?
Cover is the #1 place for heat loss.
2. Consider adding a foam thermal blanket that floats on the water.
Costs a lot less than upgrading the cover. I just roll mine up and jam it next to the cover, no problem.
3. If you do decide to "stuff insulation", bag it in heavy duty bags as Tman122 says. Also consider Roxul instead of the pink stuff.
4. Is the "metallic" blanket affixed to the wood panels or to the frame?
If it is on the panels, see if you can wrap the frame. I was able to wrap the entire frame in a single sheet of Reflectix, cutting out just holes for the contact points to mount the panels.
Note that two layers spaced close together but with a slight air gap will provide better insulation than two adjoining layers.
5. You can easily make panels out of R board, but it might be best to securely bag it as well to prevent insects from making it a nesting site.
6. Get an IR thermometer. They are inexpensive and can easily tell you the spots you are loosing heat.
It's easy to pinpoint the top lip of my spa as the primary place I have heat loss.
You could probably do everything in steps 2-6 for less than $200.
If you want to increase the budget:
7. Foam your tub. Hire a professional or get a do-it-yourself spray foam kit.