There are some hotels around the campus that might offer extended stay. Alafaya is the main road, so perhaps start your search there? Also University Blvd?
I would caution to not look just at price alone, because some of the areas near UCF are a bit sketchy, but they will be right next to nice areas. So don't get the cheapest place, and if it has security, all the better.
Has your son contacted the continuing education department? Maybe they might have some ideas?
I am not surprised that there is no space in university housing. My daughter attends UCF and has to live in an off campus apartment. She transferred in over a year ago and has not been able to find housing on campus, even though she applied for it and went online to reserve the moment it opened up. There are very few on campus options, and way too many students. I don't remember the exact numbers but something like 7,500 people can live on campus, and 60,000 attend UCF. Many students have a good long drive to get to class because everything close by fills up very quickly. Hence my thought on an extended stay hotel.
One other option may be to search on UCF's Reddit discussion site for short-term rental or sharing an apartment?
https://www.reddit.com/r/ucf/
Thought of one other option - there are two (that I know of) complexes that are UCF affiliated, meaning they only rent to students and you must follow all UCF rules, plus the shuttle runs to and from campus to the complex. One is Pointe at Central, the other is Knight's Circle. The Pointe is a bit further, but has the shuttle and has less of a reputation for trouble. Maybe they will have a short-term option?
Good luck!