I was wondering just last night if there were any SF members from outside North America.
As someone who is always looking to clear the next level of SF, I am sympathetic to your drive to move up.
There is nothing wrong with dividing your pull-ups into manageable chunks.
As for form, the instructions for SF say "Speed should not come from fast movements, but rather from less rest between exercises"
and the description of a pull-up reads:
Grasping a bar, pull your body up until your chin clears the bar, then finish by lowering your body until your arms and shoulders are fully extended. Use whatever grip feels right and it is often good to alternate grips.
So the prescription is controlled pull-ups from a dead-hang. But I get the feeling that form gets compromised on D3 quite a bit.
I think you have to keep track of your own progress. If you can bang out the requisite D3 pull-ups (and push-ups and squats) in less than 5 minutes, that's always a good thing, but if on D1, and especially on D2, you are not using excellent form, then you have to wonder what kind of strength are you really developing?
In my case, after 19 weeks of SF, I came to a decision regarding pull-ups (palms away from the body) and chin-ups (palms facing the body). I had known this all along that was considerably weaker when performing the former, but I kept hammering away doing chin-ups. At 19 weeks, I realized that better pull-ups weren't going to come out of more chin-ups and decided to do only pull-ups from then on.
I took a big hit on all my numbers and am still recovering (I am now on my 26th week), but my numbers are more meaningful too.