Sick Euthyroid

So, I've spent a lot of my week dealing with Simon (my one remaining cat, a 10 year old indoor neutered male DSH). He's drinking a lot more than normal, and urinating somewhat more than normal but not markedly. He is a mystery at this point. His blood work was completely normal, not a single value outside the reference range on his CBC or chemistry panel. His urine is concentrated (> 1.050) and the sediment is not active-- there are a lot of lipid droplets, less than one white blood cell per high power field and an occasional epithelial cell (not unusual for sterile free catch-- we tried for a cysto but he just peed all over us, luckily one of the techs standing by caught it midstream in a red top). His physical exam is unremarkable, with the only notable finding being that his kidneys are on the small end of normal, with one at 3 cm and the other at 3.5 cm.
Just for kicks, we ran a free T4, which came back markedly low. (I ran a T4 last spring when he had a bout of vomiting and it was within the normal reference range then so I do have one point of comparison).
So he is sick euthyroid but we can't find a reason. Seriously, Simon, do you have to this difficult?
I decided to culture his urine despite no clear signs of infection, just to rule out infection.
The next step is measuring his daily water intake to see if he is truly polydipsic and then repeating his free T4 in a few weeks.

Why can't my animals have normal diseases? Lindy had chronic kidney disease from the time I got her at 8 months and then her last two years a giant cyst on her kidney that grew so large that it felt like a bladder and no one knew what to make of it. Now Simon... Yes, I'm relieved he doesn't have diabetes mellitus or chronic kidney disease but I wish it could be something simple for once, like sterile cystitis or a urinary tract infection rather than a mystery!