Quick question for the OP....after you're done riding and pull your foot out of your boot, is your tendon really stiff? I mean stiff enough that it's hard to lower your heel to the ground?
I had the exact problem with my achilles tendon on my front foot several years ago. It was so bad that it actually caused me to stop riding for a few years and only ride when I went on bigger trips. Even then, I could only ride one day and was in too much pain the next day.
Anyway, I did find that stretching and taking advil before riding did help. However, what ultimately caused the problem to go away all together was buying new bindings and new boots.
I first bought new bindings and the problem was reduced quite a bit. Then, I bought new boots and haven't had the problem since (except for a few times when I experement with binding angles and forward lean). I now ride more often than ever before and can ride multiple days in a row without having the problem. I assume the increased support with much better bindings and boots solved the problem for me.
My guess is getting new boots that fit really well will help a ton, if not solve your problem altogether.