No clue about drugs, but do weight-bearing exercises before trying cardio. It's way more effective at loosening up muscles. And make sure that your muscles stay WARM. My muscles never loosen when they are too cold. Underarmor's winter stuff is awesome for that.
YOu are right staying warm definitely helps:) However, I've noticed in recent years that I cannot get loose at all. I'm just always stiff. So now its time to get on the meds again. I only need it for sports thats it......to be competitive. I don't even need it for my workout sessions. Only when I compete which is 3 times a week:)
Try Flecanide Acetate. I had the same problem as you where Mexiletine worked for a while but then I had to increase the doses so much it got dangerous and had to come off it. Carbamezapine did nothing either.
I'm 19 and now take 100mg of Flecanide twice or three times a day and have done for the last 6 years and it is brilliant. It also works instantly so if you miss taking it for some reason or are having a bad day and need to take more, it starts having a relaxing effect after about 20 minutes. Flecanide isn't licensed for Myotonia in the UK but it is as an antiarrythmmic drug and might be easier to get hold of in the US. Definitely worth a try, you said you play basketball, I play netball so pretty similar and really struggle without flecanide to the point where I stopped playing at school. But I started playing again and after warming up and as long as I keep running around the myotonia is almost unoticable which is an awesome feeling!