Like others said, standing tumbling is probably really important. Yes, you should start working tucks, but it would probably not be all that hard for you to get standing multiples and jumps to bhs. since you can already do a backhandspring, it would just be a matter of connecting them to other backhandsprings or a jump. This is the area where they need full squad tumbling, and it will probably be easy for you to pick up.
That being said, you should still try to see if you can start working tucks. Not everyone will throw a running pass, but they're more likely to put you on the team w/o a skill if you've at least worked it.
You should try to see if you can get a stunt group together at an open gym and work on level three skills. You may be a strong base at level 2, but you will need to show them you can base level 3, and to do so you need to practice. So see if you can practice basing single legged stunts that are extended! Also you'll need a lot more bravery in level 3, a flyer will be twisting toward you (Full downs/full baskets) so you can't shy away from a stunt! I think that even though the action isn't much different as a base from a straight ride/straight cradle, you should practice them a couple times to get used to having someone spinning at you. It can be scary at first!
There are also triple jumps in level three, idk if they're legal in level 2, but they require a lot of strength so working on your jumps would benefit you too, just stretching and doing leg exercises to try to make them as good as possible!
Good luck! I think if you practice the stunts and try to get the standing tumbling you could definitely make a level 3 team!
