Hmmm.... hard to say exactly but let's give it a go.
First off, getting your bum too far off the seat may not or doesn't help as it much as it hurts. This would be rider dependant though, we all have seen some MotoGP guys nearly completely off the bike. But for us mere mortals, we might want a more conservative approach. Next along the same lines, getting too far off can make your grip on the bars too tight as you may lose your good lock on the bike. So when the 003's let loose, the tightness on the bars can make it harder for them to regrip or cause a slip where there would normally NOT be one. I speak from experience here, as 003's used to be my tire of choice. Isn't their loose grip awesomely fun though?
Next thing is very, very, very subtle but important. When you hang off to lessen the lean angle, do you still subconsciously use the same amount of lean anyway? I ask because I noticed that about my riding some time ago. I was in error trying to chase "Peanut's" (talented ninjette member) super duper lean angle on his 250. I wanted to be able to do the same. Let me tell ya, hanging off but not increasing lean is a hard mental thing to get over. Everything in my head was telling me to turn and lean to make the corner. Allowing the riders weight to do some of the cornering work takes some specific time and attention to skill building.
Next, the "pick up". In all honesty, I try to spend as little time at max lean as possible. Why is that you think? What are the benefits?
For completeness, I have to ask about what rearsets you have. Stock? Woodcraft? After each track session, if there are pics available, I review them specifically for "low hanging bits". To me, it falls into the category of "an ounce of prevention, is worth a pound of cure".
Bike Geometry, many of us racers here have raised the tail of the bike about an inch for added lean clearance. Have you put any thought into that aspect of your setup?
Lastly, let's quickly address tires. The tire you run can be a fickle thing. I have been beaten by lesser riders on 003's and have nearly lapped better riders on better equipment while myself running 003's. In the end, it just became too sketchy for me at the edge of crashing every session/race to continue my relationship with the 003's. I swapped to DRII's (front and rear) for a time and the same love hate relationship happened but only with the front. I eventually swapped the front for a 110 supercorsa but... I will be changing that to a 120 next season as a personal preference thing.
Speed: Interestingly enough, I ran some of my best times on a stock bike with 003's. If "I" could just get them to grip just a bit more at full on race and lap record paces. With my current setup, I leave the track with about 2mm of chicken strip still there.
What pace are you trying to push the 003's to?