As you thought, spinning the cylinder is a good thing to avoid. Ideally, after setting the hammer on the half cock notch, you'll cowboy load the cylinder - load one, skip one, load the rest of the way around to the first one - then close the gate, and index the cylinder to the next notch, which will let you lower the hammer onto the empty chamber. No spinning or excess movement of the cylinder involved.
As noted in posts above, fanning the hammer puts more wear and tear on the lock work in general - although not specifically just the hand - and avoiding it is a good idea as well.
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I don't think any of that is your problem. There's a reason that flat springs have generally been replaced by coil springs in most firearm applications. Springs in general are tough to engineer and then manufacture properly to get consistent results in the first place, and coil springs in general will last a lot longer before taking a set and or suffering fatigue than a flat spring.
If you look at a schematic for a Ruger Single Six you'll notice the cylinder latch spring, pawl spring, hammer plunger spring and trigger spring are all coil springs, as is the mainspring for the hammer. The gate detent spring is the only flat spring left in the whole revolver, and it is not all that critical and can be over built for what it has to do.
In the Single Six, the pawl is essentially the same as the hand in the Heritage revolver, and as you've discovered, redesigning the revolver to use a coil spring makes a significant difference in longevity.
Given that you are not abusing the pistol, and that you seem to be pretty good at replacing the spring, I'd recommend just ordering a half dozen hand springs, along with a couple hammer springs as sooner or later you'll probably break one of those as well. It will save you some shipping and it will save you some down time.
I've never had to replace anything in my Single Six, but then again they are $580 pistols, and for four times the cost of a Heritage I expect a much higher level of reliability. The Heritage is what it is, and for $150 or so they still offer decent performance for the money. As you've discovered, it won't run forever without breaking, but there's also nothing wrong with replacing a spring or two now and then to keep it running, and as long as it gets the job done for you, just keep shooting it and repair as needed. If it gets to the point it's worn out, won't keep time, the hammer start slipping onto the half cock notch, etc, then you'll know it's time to replace it.