All I have to say about any of this, is that ya'll have some well trained dogs if you can stand at a fence and call them off when they're looking at a hog.
If they are looking at a hog that is when I will go get the dogs. The barking may get a land owner to shoot them thinking they are barking at his animals. Plus if they are on the pig they could get hurt. I can call dogs off a track but looking at a pig is different. Just know if you jump that fence you are wrong. That is why I drop any knife and mule tape. Because I know I am wrong but I am choosing what I feel is less wrong. But if a land owner or the law shows up I will show respect and admit I am wrong. I don't have GPS but I start calling them when they get too close to a fence. I have been lucky and never had a problem by the grace of God.
I understand why you drop the tape and knife, but when you get to the bay, if they are in fact bayed up. How are you getting your dogs if you're alone. I could see flipping and holding the hog until the dogs are off if you had help, but I can't think of a way to do it by yourself unless you kill or tie the hog.
Also, I believe trespassing carries a simple (cheap) fine if prosecuted. Then again, you've got to be caught first, then prosecuted, then convicted. Most people I know that own land and have been on that side of this situation are reasonable people, and wouldn't go through all of that if you're honest and forthcoming as to why you are on the land.