This is certainly possible. Ensure you are priming the pad adequately, and reduce pressure on the DA as you finish a polishing cycle. Also, before you start drastically altering your technique you may want to consider the following:
* You are using a line of products that are recommended for a rotary polisher on a DA. That is not to say that it cannot work, as you state in your original post that you are pleased with the finished results, but you may want to try again with a DA-friendly line of compounds/polishes first.
* You are moving from a compound directly to a finishing polish which seems like a big jump, why not instead move to the next step polish in the 3M system (3M Extra Fine)? This should level the compound induced marring quicker than the Ultrafina, therefore negating the need to work the Ultrafina beyond its buffing cycle. Depending on the level of defects the compounding step may not be necessary, likewise, the finishing step you are using Ultrafina for may not be needed, as the 3M Extra Fine Polish may produce the desired gloss. A test spot will be the indicator on the best approach here though.
Keep experimenting and let us know how you make out.
Best,
Shawn