@doublebubbletrouble , we went through a variant of this for middle school, so while I can’t give you advice on what to do, I can share a couple of guideposts that came up for us.
Normally, I would say you should choose the school that has the better education for next year. BUT if you are pretty sure you’ll want to pursue BS in a year, I would NOT choose the day school, first for the social reasons mentioned upthread but secondly because your kid might like it and want to stay. If I am reading right between the lines, the day school set up is really challenging given that you are a single parent, and BS – with everything academic, social, athletic and EC “under one roof” – would be more enriching for your son.
If you REALLY want a boarding option, don’t get thrown off that path.
And if that’s the case, I would see if that can happen even for next year. It depends on where you are and what you want, but there are schools - and good ones at that – that entertain late applications for compelling reasons. I would second the idea of getting a good consultant to help you out with that. They know whuch schools and which reasons – they can save you time and nerves as well as give you the best idea of what to expect.
I feel for you. Hard choices and many unknowns. Wishing you luck.