Great question. Panic attacks seem to be becoming more common, so your question is quite timely. Too, it sounds as though you have been down the road of therapy (both self-guided or with a professional) and are onto some good suggestions.
The one aspect you did not mention is controlling your thoughts during the attack. Activating the parasympathetic response through physical exercises like the ones you mentioned is absolutely essential, but often times a person in the throes of a panic attack is also going haywire between their ears - in other words (and I did not mean to be glib), the anxiety is being shot up because of intrusive thoughts that basically convince the person that they are either in grave danger, or (literally) that they are going to die.
So to answer your question directly, I would recommend going through some mental visualization exercises meant to encourage relaxation. Find the scenario that works best (and fastest) with you, and begin to take control of your mind while you are doing the breathing and stopping. Arrest any thoughts which drive anxiety ("I am going to die," "I am having a heart attack," "I cannot stop this attack," whatever it is for you). And this sounds rather simple, but it takes some practice.
Lastly, it seems that folks who tend to bottle their emotions up are more prone to panic attacks. So if you are an internalizer, I would also recommend finding safe outlets for the anxiety or tension you experience throughout the day. Allow yourself to relieve the pressure rather than continuously shaking the sealed soda bottle.
And remember, all the technology in the world still has not identified what exactly is the mechanism that triggers these sympathetic arousal attacks. You may be dealing with them for awhile, although the current research seems to show that the attacks lessen in duration, frequency, and intensity as you age.
I do wish you well. If you are satisfied with the response, please hit "Accept." This is the only way I receive credit for my answer. Thanks-