Usually any kind of browing is a reaction to GOOD lighting. Even though it may not look as nice as the white, its a zooxanthellae reaction.
Your BTA is going to require more frequent feedings to help him along his way. Your feeding cycle would accomidate a HEALTHY BTA but not a sick one.
Feed a variety of meats: shrimp(chunks- not just mysis), clam, silverside, and even things with a shell like krill. Diversity is key. I would also soak the food in a nutritional soak like Selcon or Zoe just for the kick.
Dont move him, move the lighting to accomidate him as best as possible. If you have a bright direct light, try to direct it to him, or place it right over him on the tank top.
Maintain good flow, and try not to make any 'changes' to your tank in Powerhead positioning or rock-scape to avoid added stress.
Try to keep water quality pristine.
Is your 44g a 5 sided corner? Mine is a 44g and its a corner unit that is tall (like 25" deep tank) I think you may have the same one.
Getting the bright light to venture to the bottom of the tank can be tough with that depth, but you do have a nice MH so it shouldnt hurt your tank at all.
This healing process will take time and patience. Remember not to overfeed the BTA or he will vomit it back up at night time and that peice of food will rot in the tank while everything is sleeping = bad water quality.
Good Luck! Keep us posted.
Try to take pictures ever so often to monitor his progress, sometimes its easier to tell if he is improving over a long period of time if you have pictures to compare.
Jessica/Shrimpi