The OP asked for something slightly more stable than a stalker. I'm taking that to mean slightly more over stable. The TB/TL that many people are mentioning are more of the same ball park than they are more overstable.
A disc that hasn't been mentioned that you might want to give a shot is an orc. It's a disc that has been around for a long time and I have been finding it very reliable. It only has a little bit of high speed stability, but it has pretty good low speed stability...a pretty good fade, which I think is what you are looking for. The high speed stability should be plenty stable enough in 300-330 ft range you mentioned.
It has the small rim you require and it is easily found in star plastic. I only throw around 350 on average and it has replaced the starfires I used to use as a stable driver. It is worth a shot. Good luck in your search.
I'm a big Orc fan, have been for a long time, but it's more of a driver than I'm looking for with this slot.