@edgarblythe,
Quote: but cannot tread the water for more than a few minutes. My body is not a swimmer's body.
From your pic, Ed, you look to have a good bod for swimming. The problem with the old method of teaching swimming is that folks were taught to way overdo it. Like everything that has been learned well, slight movements are what's best, not the overly active motions, which are energy consuming and self defeating.
But snorkeling makes everyone a good swimmer because it removes the frightening feeling that scared swimmers have - "I can't keep my breathing holes above the waterline".
First, treading water is unnatural. You don't see water animals trying to frantically keep their heads out of the water. The difference between being comfortable in water and being tired and scared is really tiny.
I've often done 5 hour snorkel floats where in water time at one time has been over an hour. Even without a snorkel, it's easy to be in the water for as long as one wants, subject, of course, to hypothermia concerns.
The secret is to keep as much of your body in the water as you can. Think alligator. Stay relaxed. A relaxed body can stay afloat just by keeping one's lungs naturally full. Breathing out will cause a slight drop but by the time you take your next breath you can stop the drop.
A body with muscles tightened by fear is effectively a stone. Combine that with a raised appendage, an arm say, and that will cause a body to quickly go underwater. When one's brain thinks "I can't stay above the water", drowning isn't far off.
The waterline, in my static lung full position with all body parts in the water is below my top lip. Breath out position, I drop to eye level, breath in and I'm back to lip line.
Combine that with a snorkel, which obviously moves your breath hole that much higher, and you can take smaller breaths which will put your static hold line in the middle of your forehead or a little higher.
The other super important part, when you are sans snorkel, is to breath with a wide open mouth which prevents sucking in your breath, and water. Then any water that falls in by gravity doesn't cause a choking situation. The air, being much lighter, moves past the water without pulling it along.
With a wide open mouth, at the bottom of a pool, I can breath right off a scuba tank with no regulator on. I just crack the valve a little and breath in with small, wide mouth breaths.
The whole process is all about nuance.