It is possible. Although i don't tumble anymore, and never got any tumbling skills that i could be proud of, coaching kids i see two types of girls:
The naturally talented ones that learn really fast, can fix problems (take corrections) in one practise and move on with their tumbling skills.
And there are the girls that have big problems with tumbling skills, even if they are dedicated and want it really bad. Just seems like they need much longer to controll their body and know what they need to do to hit the skills.
So the question for me is:
How long did it take you do almost get your bhs?
Do you feel like it's easy for you to take corrections, how good are your other tumbling skills like front walkovers or your round off?
And the step from 2 to 4 is not just tumbling like mentioned before.
Don't know wheter you fly or base, but it's body positions, strenght, timing, jumps (toe to bhs) and faster routines.
If you want it really bad - go for it. And keep in mind that one season in level 3 would just make you better prepared for level 4 :-)