Not sure why dimmable in a gym as for fixture I would go with a track maybe even in a squre to give good light where you need it instead of a center light that makes shadows The nice thing you can run a lot of LED heads from one feed

I tried to find LED flush mounts for you that satisfy all your needs, but it is difficult, especially the lumens...

This Maxim Lighting flush mount has a 3000K color temperature, but only 1900 lumens. Price is $298, so above your price range, but we do have 10% off it right now.

This Access Lighting flush mount has 3000K, but 1290 lumens, $140

This Access Lighting TomTom has 3000K, 3057 lumens, $292

Access Lighting Tara has 3000K, 1515 lumens, $216

Access Lighting Orion has 3000K, 1515 lumens, $196

WAC Tube has 3000K, 1740 lumens, $279

TomTom is probably closest to satisfying your needs, but does fall short on lumens and is a bit too high on price. I like Patricia Colwell's idea of using a track fixture instead. I hope this is of some help!

Many thanks to both of you! The reason I wanted a dimmable fixture is that I am a cyclist and will be riding my trainer in this room--often while watching TV, so being able to work on my bike in the bright light but ride it in the dimmer light would work best. I'll check out all of your suggestions, thank you!