Your BO is raising a ridiculous ruckus to get back at you for leaving.
I never get these kinds of conundrums. It is not a horse prison. You have more control than the BO, because you can move your horses when you are ready. Deal with the rest of it later.
What you really want out of this is avoiding a verbal confrontation with BO. That is about timing your leaving, planning it efficiently, as well as avoiding the BO and being matter-of-fact and distant when you can’t.
The board contracts were done separately, so they are separate, independent. As an example, you could have sold one horse and kept the other, without modifying the contract of the horse who stayed. The boarding and the monthly board payments happened concurrently, not consecutively. So the notice period is the same, concurrent, not consecutive. Hope that makes sense.
Not a lawyer, but have handled many business contracts in the course of doing business. This is a silly argument by the BO to cause trouble and maybe bully you into another month of board for both horses.
How exactly does this BO “stop” you from leaving? You don’t need the BO’s permission for any legal or other reason. They are your horses, put them in your trailer and go. If you manage this properly and the BO doesn’t know or anticipate the leaving moment, and especially if BO isn’t even there, then you. just. load. and. leave. Move it up a few days if you need to (or a week or two) to help you with the timing and avoid awkwardness.
As has been said on these boards many times, if you can manage it, just pay double-board for whatever period you can afford, so you can move the horses before the end date. Don’t notify the BO exactly when you are leaving to avoid an awkward and pointless confrontation.
The easiest for all parties is that you leave when the BO isn’t even there - easier for you, easier for the BO. Leaving early leaves the BO better off financially, because you paid for that month and aren’t using the feed. And the BO can go ahead and fill the stall (although this BO may not have many takers if the word is out).
Make sure that your actual leaving is a fast process. Quick load & go. Get as much of your personal stuff out early as you can, so that whatever is left is loaded fast when you take the horses. Start getting your odds & ends out now.
The legal aspects go with your state, as mentioned above, but keep in mind that anything legal begins with the BO and requires their time and money to initiate. The BO knows she/he has little chance of recovering much.
Do not make a bigger deal out of this than it is. You are moving your horses, do what you know is right (30 days notice per horse is a concurrent 30 days, not consecutive), don’t argue with the BO, just make a plan and move them.
Good luck on a smooth transition! 