There's a simple tool you'll need to modify these settings, some of which are not accessible in the in-game options.
Link(Realmware BF3 settings editor):
http://bf3.realmware.co.uk/settings-editor/The latest version is needed. Simply navigate to 'key bindings', select 'jets' and look for these variables: 'Light Brake', 'Heavy Brake/Hover' and 'Hover'.
At default(in-game), Hover and Light Brake are both assigned to the 'S' key while the Heavy Brake is inaccessible. Simply change Hover to unassigned and bind Heavy Brake to a key of your choice(I used Ctrl)
The Heavy Brake works to slow the aircraft down to ~100(the default light brake brings it to ~200), and for the F-35 works the same as Hover so there really isn't a need for a seperate Hover key.
You can also reassign the Q function to any other key or use Spacebar to Pitch up instead of fire.
Happy flying!
The software I've been using for over two weeks now, and it's definitely safe to use with Punkbuster. I've also tried playing with the keybindings changed for more than an hour. They worked and I did not get kicked. The program simply changes BF3 user settings and does not alter anything else.
However, it is clear that Heavy Brake adds a whole new dynamic to jets which DICE apparently left out from the game. This may not have been intended for online play or been disabled for some reason. Maybe crash or demize can comment on that.
I'm a complete and utter noob whose game is already broken due to stuttering issues(which I'm desperately waiting for DICE to fix

). I can't say if these fixes will indeed make the F-35 on par with the SU-35... or any other jets any more effective. I still got blown out of the sky every time.