What is long? When you use a
DAS you come back and go into the FP line. This will still mean waiting in a line that is crowded and full of people. The FP line could easily be 15+ minutes on its own as it is simply supposed to be shorter then standby (and this happened even before the new FP system).
What causes the anxiety? The crowds themselves? Not being able to "escape" if needed? Something else? I can tell you for me it is a mixture of being in the crowd and a feeling that i can not get out. I have had panic attacks at disney before (at les chefs because the jerk kid behind me wouldn't keep his chair pulled in so i has no space for example).
A good touring plan has done wonders for me in the parks. Way more then a DAS ever would. A touring plan and using FP really really helps for avoiding longer waits. I suggest Easywdw and Touring Plans for these things. I also do not go at the busiest times of the year because i know the crowds would be too much for me.
Do you have coping mechanisms in place to help? Have you seen your doctor or a psych? Are you taking medications? I am not asking for answers, but simply wanting you to think about it. Talking to a psych and getting on meds was the best thing i ever did for my issues. I just want you to look at all avenues to help you out... and not just for disney.