Hey Scarlette I have the exact same problem with Biscuit! My trainer told me to throw the treat (not too far away and easy to find) so that my hand is giving her the treat. At first I couldn't see the sense in it but it worked....she's off food rewards!
So example....I put my hand on the ground and say 'drop' with the treat in my hand that is on the ground. She drops cause she wants the treat. So I throw the treat and when she is going to collect it I get another one out ready. As she is coming back to me I say 'drop' with my hand on the ground again. If she didn't do it straight away I took my hand off the ground and looked away from her for a few seconds then repeated the drop with hand on ground...throw treat away. Pretty soon she was coming back and dropping straight away and once she got used to that method of rewarding (one training session) I'd say drop with an empty hand and then throw her the treat. If she wouldn't drop I'd show her the treat with the other hand (the one not on the ground) and pretty quick it got to the stage where she'd drop on command no matter what cause she didn't know which hand the treat would be thrown from or if she'd get one at all.
I also started adding things, so I'd make her drop, say good girl (which would be a signal for you) then make her sit again and then reward her with a treat. I started doing that once she had the basics down pat to her brain think and now she's quite happy to do lots of tricks in a row cause she learnt that I'm the one that decides when she is clever enough to be rewarded. She also learnt that only when the treat bag was out and we are doing training sessions does she get a treat...otherwise it is just expected of her and I don't give her a treat for the things she already knows, only the new stuff she is learning.
eg on that one (sorry if this is so confusing....let me know what you don't understand!)
she learn to do an army crawl along the ground right now so I get her to drop to get her into position and then get her to crawl and she gets the reward for crawling, not for dropping.
I might just stop here before I confuse you anymore!!!
Ask any questions you like cause it's probably hard to visualise.