When I started my system over 6 years ago all I had was a 36" T5HO fixture. I added my GBTA after a few months of start up, probably should have waited a tad longer but I was a newb & didn't know any better. Nevertheless, the BTA did reasonably well under those lights. It was not as bleached as yours when I purchased it & it really didn't lose any colour under the T5HOs. At one point, for some unkown reason, it decided to move to the back almost under a rock where I could barely see it. Let that go for about a month until I could see it was bleaching & shrinking back there. Bit the bullet & re-arranged the rockwork to get it back under proper light & it recovered nicely. Also pretty much stayed put after that.
6 years later I've gone through some lighting upgrades which included adding 2x250 watt MH & bumping the T5HO factor up by adding two 48 inch tubes with individual reflectors. Since April 2012 I've been running a DIY LED fixture using 27 ten watt multi chip LEDs. The lighting increase was more to enable addition of light hungry coral rather than for the BTA. It has split numerous times & the clones I still have in the tank are now very large, to the point where they're taking over & stinging coral. At some point you might consider adding more light, but I don't think that's your main issue at the moment. You simply purchased a very bleached specimen & will need patience & a bit of good fortune to get it coloured up.
BTAs can be pretty tough customers, surving powerhead incidents etc., but sometimes a funky paramater can mess them up in a hurry. Seems like you're on the right track with small feedings. I no longer feed mine much these days & when I do, it's every couple of weeks with silversides. It would be good if you could confirm that it's expelling waste from time to time as well. It could be that it is spitting out what you're feeding when you're not watching & not properly digesting. Best you can do is keep feeding, try not to overfeed, wait & observe.
Here are some crappy photos of my specimen(s) to give an idea of the amount of colour that would be considered normal. Both of the following were taken some years ago.
Here's something more recent, this guy is almost the size of a dinner plate when fully inflated under mid-day lighting.