Thanks Bruce. Those are interesting. My wife is on her way to Tractor Supply right now to buy a couple of the ratchets so I'm going to try those first. Hopefully they don't cut or snap the wire. I'll probably buy some of Jake's as well and do a little comparison (as I suspect the fence stretching ain't over yet.)
To keep the real problem in perspective, the new owner is better than the prior. Except for some fence damage, he seems to stay on his side and I don't see evidence of anybody wandering around my ground. With the prior resident, it seems like I'd pick up a beer can every other week and little things were disturbed. And the new owner is definitely taking much better care of his property. The big oaks have been trimmed, the front door replaced, the back porch screened in, new gravel on the drive, the grass around the house is cut.
I just don't like my fence damaged. Still, in the grand scheme of things life is pretty good and I'm getting great recommendations on how to tighten the wire. As I tell the old farmers in the area, "I'm a city kid. I don't what I'm supposed to be doing but I'm going to keep trying things till something works."