Congrats on your recovery D1!
I didn't mention that in my vast array of studies (spent decades being a professional student) I went through a Polysomnography program. Made it to the end and decided I didn't like staying up all night watching other people sleep! In the Polysom world it's called "sleep hygiene" and it's very important. It involves keeping the same schedule as much as possible. Have a set routine that you go through every night before bed. Don't read in bed, don't do games on your phone or computer (like my DH). Bed is for sleeping. Try to get away from the television and computer at least 30 - 40 minutes before bedtime. Don't keep a radio or TV going during the night. Something that creates "white noise" is fine though. You need several hours of uninterruped sleep before you can get into a REM cycle. It sounds like that may be where your problem is....you're not making it into REM. Have you considered that you might have sleep apnea? Do you snore? Do you grind your teeth? Ask your wife if you snort or startle yourself awake after a period where you stop breathing for several seconds.
Melatonin works great for some folks - not so much for others. (It gave my DH horrible nightmares.) Warm milk really can help some folks. A warm bath before bed - even though most men prefer to shower a bath can be very relaxing - especially with some lavender scented bubble bath!
SL is right. Try aroma therapy. We have a lavender spray that we can use on the pillows and it really does help. Get out of bed if you don't fall back asleep within 15 minutes or so. While you're up try to stay relaxed. Don't get up and get really busy. If you can, stay away from bright lights and television. A boring movie or a book certainly may help, but be aware that the flickering lights from the television may wake you up even more.
If all else fails - have a sleep study done. It can be life changing. Most of the folks with sleep apnea follow the pattern that you describe. They fall asleep easily enough because they're tired from not getting a decent night's sleep the night before. But then, they have the pattern that you're experiencing. Most insurance companies cover the study.
If not here are a few tips for combatting apnea. DH had horrible apnea, both obstructive and central apneas. He would stop breathing over a hundred times a night and sometimes wouldn't start back until his oxygen level had dropped to an alarming level. I don't have any idea about your physical build - but my DH was overweight with a very thick neck and he slept on his back. If you sleep on your back gravity works against your throat muscles. They tend to 'collapse' which causes the gasping that wakes you up. That's obstructive apnea. Try sleeping on your side. Try the 'breathe right' strips. Also you might try a humidifier in your room.
Also, he's lost about 35 lbs recently. We spent the night away from home unexpectedly a while back and he didn't have his c-pap machine. He barely snored at all.
Okay, lesson over!
Sleep is so important to our physical and mental well-being. I hope you come up with a simple solution to your problem. Try all the easy things first, but if that doesn't work for you - you might really need a sleep study. Lack of sleep can cause a lot of other health issues.
The first night my DH slept with a cpap machine he woke up the next morning and was ecstatic. His first words were 'now I finally know what it feels like to feel good in the morning'....
Sorry for writing a whole book!