You should be able to find something decent outside the cities and most desirable suburbs for that rental budget. If you are open to flats that will give you much wider options too. The priority really has to be school catchment. Your older kids can travel to you but not all schools will be able to offer all subjects in 5th/6th year in more rural areas, some will run them as a consortium with other schools in the same region.
Not all schools will be a particularly welcoming environment, identify some areas then ask here and research/visit for specific experience.
Also, if you move your son directly after GCSEs it would be a good idea to get him to Scotland as soon as the final exam is over (mid June for most I think). Scottish students sit their exams in May and commence their next year of study - Highers - at start of June so arriving in August will put him on the back foot immediately as likely to have missed a topic in every subject.
Off the top of my head - schools with a fairly good reputation on the west coast between Helensburgh and Maybole.
Clydeview academy in Gourock
Largs academy
Prestwick academy
Kyle academy in Ayr
All of these towns are on the coast with amenities, gorgeous views and have train links to Glasgow. The ones further south might actually be quicker by train/car due to faster lines and m77.
GCSE to higher is perfectly doable for a kid who was planning on A level, but need to get him started in June and identify any gaps from his GCSE spec and Nat 5 equivalent to address in the summer so not behind peers. It will be a much harder year 12 than he was anticipating as highers are one year (more like 9 month) courses.