Yes, obesity could be the sole reason for your labs but as KS suggested you may have other issues as well. Obesity is always a dead end in terms of health and it's not IF your health with fail but WHEN your health will fail. Obesity affects every organ system, deranges nearly every endocrine system, and is probably THE NUMBER ONE cause of all chronic disease.
As for diet. Assuming there isn't something else going on I know you think you "try and avoid sugary foods" but what exactly does that mean to you? Are you talking about avoiding soda and candy but a pound of pasta and a loaf of bread is OK? Or are you talking about no pasta, no breads, no starchy vegetables, no simple carbs and you try and eat all complex carbs?
There's a fact that needs to be dealt with here.....no one becomes morbidly obese eating appropriate amounts of low glycemic-index foods. It just doesn't happen so I urge you to really cut out most of the simple carbs as they really don't have much of any place in the human diet IMHO. The paleo diet is a good place to start....I'd say I eat a paleo-like diet and I like the reasoning behind it but I'm not a nut job about it either.
I also track calories daily but the interesting thing is on the paleo diet I need to track calories to be sure I've eaten enough.....not too many.
I know you haven't had any elevated glucose tests. Think of insulin resistance and type II diabetes as a continuum. People eat high glycemic index foods and that increases adiposity. Visceral fat stores build up and the pancreas just keeps pumping out insulin. Eventually high visceral fat stores start dumping large amounts of free fatty acids into the hepatic portal vein and you get inflammation and fatty liver (elevated ALT).
From this point on in response to the inflammation and increased adiposity the peripheral body tissues decrease their insulin sensitivity in an attempt to stop fat formation and limit weight. Peripheral tissues stop taking up glucose and serum levels rise. The pancreas responds to this increased rise in serum glucose by trying to pump out even more insulin until eventually it can't pump out anymore and frank type II DM sets in.
Your are correct that many with insulin resistance with have normal or high normal fasting glucose tests but elevated if you do a glucose challenge and also C-peptide will be elevated. This is a marker that is made along side insulin in the pancreas and when it's elevated with normal fasting glucose it means although your pancreas is able to keep up with demand it working really hard to do so.....that is in a nutshell insulin resistance. I'd have your C-peptide checked too.
As for sleep apnea. The basic idea behind low t and sleep apnea is LH is released in a pulsatile manor during REM sleep....if you're having apnea that is disturbing REM sleep you may not get any (or very little) LH release and thus little if any testosterone production. This is also the proposed pathophysiologic mechanism behind poor sleep or sleep deprivation and low T.
In my mind, obese guy who snores with low T.....couldn't makeup a better candidate for sleep apnea. I'm amazed not a single physician has mentioned this to you - it's about the only thing all my doctors consistently brought up and I barely snored at my heaviest. If you decide to go on TRT I think you really need to be evaluated with a sleep study as TRT can make mild sleep apnea worse.
My 4 cents.....as has been said.....almost all doctors suck at treating these issues.....educate yourself.....let your physicians help you as much as possible but as you can read on this board most people here need to go "out of bounds" occasionally to get what needs to be done....done. This may be the AI that you need but your doctor won't give you or whatever. The key is educating yourself!