If I were your BO I'd appreciate you discussing the situation with me and seeing what we could work out.
At my big boarding barn, we typically had a waiting list so I was pretty firm. We required formal notice. In other words, don't tell me you're leaving until you're ready for me to give your stall away. In practice I would typically call the first person on the waiting list and see how much notice they needed to give at their barn, and only hold the current boarder to that rather than the full 30 days specified by our contract. If that makes sense... I'm giving up coffee in the morning and having trouble with coherency this morning.
YMMV though and it's always good to know what you're dealing with and what your BO will hold you to. We were maybe stricter than some as we had a lot of student boarders so a lot of people came and went as they transferred or graduated or went home for the summer or whatever, so these sorts of situations came up a lot. It also depends on what kind of client you are--if you have other horses there, have boarded there a long time, pay on time, etc. you might be cut a bit more slack.
Talk to your BO and see what he/she says, they may be willing to work with you and work something out.
Different situation, but when I was moving my 2 out of the boarding barn and bringing them home, I did not have a firm 'moving' date (depended on weather/when the barn was finished and the fence up). So a couple months ahead, I gave the BO the heads up, "hey, I'm going to be moving my guys home sometime between months x and z, but I don't know exactly when. I'll keep you informed as it gets closer." So I just kept them updated with progress, and about 4 or so weeks ahead I had it pretty well figured when I should be leaving with them, and gave my formal notice. They were very nice, and volunteered to keep the stalls open for the rest of the next month, incase things got backed up and I had to keep them there longer. Which would not necessairly be the case in a barn with a waiting list... but talking to them about the situation well ahead made them very willing to work with me.
Been there, done that. Just talk to the BO and tell them the situation and ask them how they would like you to deal with it. Maybe they have someone waiting to come in that is flexible. Makes a difference if they are full with a waiting list or not.