Kogeki.....
"She doesn't win until she gives a full bite and really fights for it." your quote.
Actually, she is in play, prey, so it may work. However, fundamentally, and LATER on in her training, this is not ideal.
I tell you why, because I made the exact same mistake. I go to bulldog shows and almost ALL of the people playing around with tugs make the same mistake.
The reward MUST be the winning of the toy. Later on, domination of decoy. Right now, the reward for her is "playing or fighting" with the tug with YOU. think about what you are doing. In the beginning stages, this works. However, what about when the dog goes into fight and into a bit of defence when worked real hard from a strange decoy? Where is the reward? How have you imprinted her to WIN? So far, you just taught her to fight harder to win. That is the REAL fundamental imprinting question that must be asked. More fight? More bite? (that is what you are teaching her). This causes MORE and MORE defence and no avenue to release the stress of bitework. There is no where to CHANNEL her drives. Should it not be the WINNING of the decoy's possession and later on, WINNING or domination of the decoy (stops fighting in a submissive stance)?
the thing is....in order for her to win, progressively, she will naturally fight harder, the right way, by countering in HARD, perfect targeting, deep bites.
If you want to increase her drive and make her parade with her "winning" , make it harder for her to get it in the first place. a TUG must be earned.....not given. That is why post work is sooooooo important. Make it hard. If she has a shallow fanger bite, MAKE HER PAY! (twisting movment dogs do not like). When she counters for full grip, THEN let her win.
Tug work is use to TEACH the dog how to win. bite deep.......win. counter in.......win. center bite hard........win. fast fast rebite......win.