There's no way a DA takes 5 times as long as a rotary - something wrong with technique and application there; maybe pads or polishes?
Yes, a DA vibrates more due to its nature but you should only be machining your car, at most, once a year anyway so it shouldn't be a huge issue; the Kestrel is well within health and safety tolerances.
Also, bear in mind the rate at which a rotary will remove paint and the increased risk of burning through/strike through.
You should use a paint depth gauge with any machine polisher but they are
vital with a rotary.
If you do want to go to a rotary, we rate the Makita above any other;
Makita 9227CB Rotary Machine Polisher | Makita Car Care & Detailing Products yes, it's a little bit heavier than some but it's still, in our view, the best on the market.
I think you'd be best to look at your pad and polish choice (I assume you're working on an Audi) and run through your polishing procedure first though and we can maybe spot something there.