Part of the problem could indeed be the conure as he may consider that a predator. Is there any way that you could move one or the other to another room?
Unfortunately there have been some health issues related with the Zilla UVB's as they don't put out the right amount of UVB, at first it is strong but the rays diminishes very quickly. Some other symptoms that we have heard about are loss of appetite, lethargy, eye issues, etc. The best fluorescent UVB in the U.S. is the Repti-Sun 10.0 and you can find that here for a very reasonable price:
www.petmountain.com Since your UVB now spans the whole length of the tank, there is no way that he can escape the rays of it. Also, a colored basking bulb is rough on the eyes, they actually do much better with a bright white basking bulb, gives them more energy which also helps increase their appetites. You can actually use a standard household light bulb for the basking bulb. If he is laying around with his eyes closed, I would suggest turning the UVB off for a few days in case that is causing him some problems.
What are the basking & cool side temps and what type of thermometer are you using? If using any type of stick-on thermometer, those can actually be off 20 degrees. The only 2 ways to get accurate readings are with either an infrared temp gun or a digital thermometer with a long wire & probe end. Walmart has the AcuRite brand digital w/probe that will give both readings at the same time as well as a humidity readout for about $12.00. It should be in the area where the plastic thermometers are, probably the garden center. What you need to know is the basking
surface temp.
For your aged beardie, you should be dusting with calcium 5 days a wk, but only 1 feeding a day and with vitamins the other 2 days a wk, but only 1 feeding a day. How long has he not been eating? It would be a good idea to pick up some chicken and squash baby food (stage one), mix a little of each with one of the supplements and a small amt of water to thin it. Heat it in the microwave to take the chill off, then use a plastic medicine dropper or needle-less syringe and put drops on his nose for him to lick off. Babies can't go very long without protein so would be a good idea to act quickly.
When he is acting better, he should be offered crickets 3 times a day, all he can eat in a 10 to 15 minute timeframe, make sure the crickets are no larger than the space between his eyes.
How long has it been since his last poop? Also, what substrate is on the bottom of the tank?
Sorry for all the questions, just trying to rule some things out so we can get him feeling and acting better.
