It sounds like her diet is already good. Whats the fibre level on her pellets? It can vary alot from brand to brand - atleast 18% is recommended.
When you say she gets pellets if she is good, is that every day? Could it be if she gets them irregularly they are upsetting her tum.
Does the mucky bum happen every day or intermitently?
Rather than changing the diet perhaps changing the way you feed it might help. It sounds like she's quite motivated by food so you can use that to get her moving. Here are some ideas:
Treatball - you can buy these for cats - there a ball with a small hole that you fill with the dry food. To get the food they have to roll the ball around gradually tipping the food out. You can try homemade ones with boxes with little holes cut in.
No more bowl - don't put anything in the bowl any food has to be foraged for. Think of it like a childrens easter egg hunt. Stick the food under/in/behing/on top of things. If they have to climb and stretch to get it or shove something out of the way all the better. I have one of those kaboob things - a metal stick you stab carrots etc with and hang up. To reach it my buns have to jump on top of a box, it swings abit so they have to move about and they take it in turns to get the best position for nibbling.
You can get chain really cheap from supply stores. The frames they sell for babies with toys dangling down on would be good to hang things from. You can probably pick a cheap one up second hand or make a similar frame yourself.
A box filled with hay with the yummy veggies at the bottom/mixed in so they have to dog for them.
I'm sure you'll be able t come up with other things. I love watching my bunnies going about getting their food. Their hay is in a hanger so they stand on their back legs to reach it. Big veggies are on the kaboob and their pellets are in the treatball. They have hay in their bed too but still go for the stuff hanging up, I guess it's easier to pick the yummiest strands or something. It means dinner times spread throughout the whole day not gobbled within half an hour
Tam