I'm not saying doing different levels is wrong but I personally didn't do it and wouldn't recommend it. I'll try to explain why I believe this.
Each of the 3 weekly workouts focuses on a different aspect of fitness, strength, endurance, speed, etc. When you start on level one, you may already have a good deal of strength but your endurance is lacking so you go up a level to match your strength limits but stay down a level to match you endurance limits. Sounds like it makes sense but for some reason I think it may result in you putting too much into your strength and robbing yourself of the ability to increase your endurance. You want to equal them out and then build them concurrently. At least, I do.
Another thing, I don't understand how you "could not do D1 at L3, but I was fairly confident I could manage D2 at that level"
There is no set number of rounds for D1 so if you can do 5 rounds of 3, 10, 16 on L3D2, why couldn't you do 7 rounds of 2, 3, 5 on L3D1? Do you think that your not doing enough rounds on D1? That should be your goal, increase the number of rounds you do each D1 workout at a certain level.
You're only in the first couple of weeks, right? Trust the program. It takes time. Do it as prescribed and work to increase your score each week. Once you can accomplish each level without assistance and can do D3 below 5 minutes, move up a level.
And can the assistance on the pull-ups. If you do 10 sets with real pull-ups, then that's your starting point. I doubt doing 26 more sets of assisted pull-ups is going to help you much at all and may hurt you. Strive to do 11 sets the next time, then 12. If you have to wait 3-4 minutes before you can do that extra set, then so be it. Or try jumping pull-ups in the later rounds, at least you're generating your own assistance, better workout.
So in summation, stay at one level until you can do each of the workouts without assistance and the D3 in less than 5 minutes. I think flip-flopping between the levels may make it less likely to measure progress and lead you to quit. Being able to say you conquered a level and move up is very satisfying.
Note that my advice might be different if you couldn't do a pull-up but apparently you can do several of them.