Hi Amy!

I'm hypo and on Levoxyl (and was when I lost the weight four years ago). I'm not sure that you have to resign yourself to 'very slow weightloss' -- I lost 122 pounds in a little less than a year with calorie counting and LOTS of exercise and wouldn't call that particularly slow.
Everyone's body is different, of course, but my doctor always told me that if my TSH was properly regulated, then I'd be able to lose normally. Once I stopped kidding myself about how much I was eating and began exercising ... she was right!
I agree with you 100% that exercise is essential for us to be able to lose weight, and especially to keep it off once we reach goal. Rather than picking weights over cardio or cardio over weights, my opinion is that BOTH are equally important for fat loss. As you said in your post, building muscle will help keep your metabolism up. But cardio is going to be your big calorie burner -- it would be very difficult to create the calorie deficit necessary to lose fat without cardio. Add in calorie counting/good nutrition and you've got the winning formula for fat loss!
My suggestion is to work up to 30 minutes of cardio 5 - 6 days a week and 3 days of weights. What are you doing for an eating plan?