I was in the same position as you last year, I took the route you plan to, for my UCAS application I was able to link my application to my school, so they were able to provide my reference(they just used my old one) for my predicted grades they let me choose, so I gave my self A*AA, for cost, I retook all three, my old school let me take it there, so it cost less, at around £400 for all three combined, I didn't get a tutor, however, I recommend you do just to be safe.
The advice I would give is to start revising early, I started revising in February which was way too late, causing there to be unnecessary stress, if you're worried about funding the tutor and exams, I recommend getting an agency job as you will be able to choose when you want to work giving you more flexibility. Also when applying to unis, make sure that they do not care that you resat, the universities I applied to were KCL, UCL, Southhampton, royal holloway, and Manchester, be careful though, as KCL and UCL only don't care if you resat for certain courses, so always double check. Also, I think it would be a good idea to mention your resits in your personal statement, such as a paragraph like, "despite underperforming in my a levels , I took this as an opportunity to.... work experience or insight days or etc during this gap year" so unis don't feel like you've just wasted a year.
My Experience,
2022 Results - BCD - Place at Aston University
2023 Results - AAB - Place at Kings College London, also got offers at Southhampton and royal holloway.
Also just remember it's better to risk another year for a better opportunity, than to go somewhere you don't like for 3 years just to wonder if you could've done better, its only one year.