hey ZeroG,
I've been suffering from panic disorder for 3 years and have never been medicated. I never had trouble working out before, although it never really reduced my anxiety. Recently though I developed more GAD oriented symptoms and an obsessive worry about my health which makes me hypervigilant and every time I work out even mildly I get huge panic attacks.
I don't think meds are going to help you. The way you can beat this is by learning to be aware of your body but not scared of how it feels. I'm working on that right now and it's going ok.
Short term solutions: I think the point is to remember to warm up properly when working out so you don't all of a sudden have a high heart rate. Because you're so used to it being a symptom of a panic attack it makes you think your having one and then you really DO have one. Give yourself a change to get used to the rising heart rate and remember that your heart is in fact normal and you will see that the panic will stop and you can just do your workout. Also, try listening to music to distract yourself.
Long terms solutions:
The best thing you could do though is to start meditating. That will help you with anxiety in every situation without ever having to take medication, but clearly it's a long term investment.
Hope that helps...