To be honest, you are on a short deadline for applying to UK colleges & uni's. Most of them have late spring deadlines for applying for admission especially for international students. You have to have an unconditional offer letter before you can apply for a student visa too. Usually that means part or all of the tuition must be paid. You mentioned one school that you had found with a payment plan...the 1st payment would need to be made for certain and they would have his transcripts to make sure that he meets the admission requirements.
Vicky will correct me if I'm wrong, but I do not believe that you can apply for a student visa from within the UK on a visa waiver. So your idea of him coming over and never going back is not possible. There was a six month visa for being wanting to explore the chance of studying in the UK, but I am not sure that exists anymore or how to qualify. But even then I think you had to return to your own country to apply for the student visa.
In terms of showing financial stability, no we did not budget for our son to work. Our application rested on our ability to support him and his grandmother's promise to pay his full tuition. Like I said, we ALL had to provide proof of that ability. Thankfully my former MIL has a trust fund for the children's education so she could do so easily.
I know how wonderful and scary new love can be, but honestly govts don't care. My husband and I were apart for over two years, he missed his only child's birth and I cried more nights than I can count while we tried to bring him to the US. In the end we got so frustrated at being apart that we moved my family to the UK, but the cost was VERY high. I could not bring one of my sons to the UK and I miss him very day even though we remain very close. I don't usually share that because I have had many people be very judgmental of my choices. I share it with you because I know how difficult these situations are but our choices are limited. Good luck!