Hi, Brian
You might try what works for me. As the years went by, I gradually changed my tuning habits to lessen any strain, enabling me at 74 (despite having a lot of fibromyalgia) to have shoulders, elbows, wrists, and hands which are still flexible. And a good back.
I sit sideways to a spinet, looking left, at about a 45 degree angle. I sometimes have to have a steeper angle if my right leg can't get under the keybed. I sometimes put my right elbow on whatever is handy,, so I don't have to hold it up the whole time.
I let the tuning pin hold the hammer, which most of them will. Put on a tuning pin it will just hang in air. I have a long extension, which gives leverage. Old spinets usually don't have tight pins, but the newer spinets and consoles can be a pain. Trying a slow pull on a piano like that is an orthopedic nightmare.
I use a lot of slapping and hitting, out at the end of the extension lever. I put the hammer on a tuning pin at about 2 o'clock, lift my hand (not from the shoulder, not from the elbow), and I give the top of the tuning lever a good whack with a relaxed hand, with most of the power coming from flexing the wrist. You'd think this would hurt my hand, but it doesn't. With experience you can tell how hard a blow will get the pin to move the amount you wish. To lower pitch, usually easier, of course, I take the lever near the end underhanded, and I use a series of nudges pushing it downward in small increments. Sometimes I put my hand right on top of the end of the tuning hammer, and nudge it that way, especially in the top octave.
Whatever action you take, it is important to instantly relax your hand after it is done. And your arm should never be tight or strained to begin with. Your left hand can make some very firm blows from right on the key, through a wrist motion, with fingers clustered. The arm and shoulder are completely loose and out of the picture.
To get the tuning lever to the next pin, I pick it up near the head and place it on.
If you face the spinet, put the tuning lever at 12 o'clock, grasp it at that awkward angle, raise your arm, and hold on tight as you try to get the pin to move without mechanical efficiency, I can well imagine you having a bad back by the end of the tuning.
Good luck ... of course we are all different, but the whacking and slapping and nudging have worked very well for me, since they greatly lessen the amount of time muscles and joints are under strain, and this approach greatly increases looseness and freedom of motion. Also, a good whack is the easiest way to get a pin to move, especially when it is tight. It breaks static friction, and since letting go of the hammer is instant when you slap it, the tuning pins don't twist or flagpole, which helps stability.