Oh dear...I know what you're going through. I've had this exact same problem with my 15 month old in the past. To the letter!!
A few things come to mind with this. You said your girl is 8 1/2 months. Has she come into her first heat yet? I found that any slight hormonal changes in my girl up until I got her spayed caused her to go through periods where I could not get her to eat at all. (She went through two heats before I got her done.)
The second thing is that it sounds like Bailey is very much a toy/game driven dog, rather than a food driven one. I can totally identify with this as well. You will have your work cut out for you, but it's just a matter of thinking the way your dog thinks. Even though it may seem like you are being "bullied" by her to play first before she'll eat for you, just bear in mind that she is wired differently than a food driven dog is. You actually really hit the nail on the head when you said that her eating is a gauge of how much activity she's had. It isn't that she's doing this on purpose to annoy you (though it probably feels like it!), but rather just that her drives dominate her in a different way.
I have found in dealing with my own fetch/toy/prey driven dog that having some form of activity before the morning meal was the best thing for her. (The point Jakoda made about bloat is very good though - do keep that in mind if you choose to indulge your girls wish for play before food.) She often will not eat unless we've had some form of intense walk/fetch/play beforehand.
Making your dog work for their food is definitely a good thing. But with dogs like ours, you will often find that they will work harder and train better when toys is the objective rather than food. In Bailey's and Junos mind, they've taken working for their food to the enth degree. Telling her to "Sit" or "Down" before they eat just won't cut it. They actually want to WORK.
On a side note, since I recently acquired a new puppy who is the most food driven little animal I have ever known, my Juno's appetite has suddenly gone waaaaay up. It's become a competition for food with the puppy though, rather than because she actually wants to eat. Still, I'm not complaining. She's kept me worried for so many weeks in the past with her picky appetite that I'm glad to see her eating a bit more!
I can't really advise getting a new puppy just to get Bailey to eat though. haha!
I'm sorry I'm not more help, but at least you know you're not alone!
Welcome to the forum!