For spring classes (i.e. Physics 152/L and Chem 122/124L), he should be fine - he’ll be able to use priority registration (register on the first day, along with graduate students) as long as he follows the Honors college rules.
I don’t think he will have an issue getting into the lectures for those classes, as long as he is not picky about his professors. Mark Morgan-Tracy for physics is outstanding.
If he can’t take PHYC 151L in fall, he can take it in spring - 152L does not require 151L as a prerequisite. (I’m not saying this is an awesome idea, just that it’s technically doable.)
Chem 124L has 123L as a prerequisite, so he will need 123L in fall. First-semester physics labs are considered much easier than first-semester chemistry labs, and students probably will drop from both during the first 2 weeks. Many lab classes don’t start until the 2nd week, and I’ve heard of students forgetting to attend in the second week, hence opening slots.
Many freshmen take Gen Chem, so unless you hear different (and great!) news when you call tomorrow, then yes, your S would be getting classes after everyone else, and the labs for that course are difficult to get. Dual credit students also register for classes the day after the last orientation, so if your S makes changes after advisement, classes may be even fuller.
I’ve read a lot of UNM documentation on overrides and cannot find a policy on a limit to the number of overrides a student may receive, so hopefully that policy has changed since @WayOutWestMom had a kid as an undergrad. It’s probably not capped at 5, as my sister who graduated 3 years ago had 7+ Capacity/Closed overrides. As a dual credit student that’s taken (including this semester’s) 13 classes at UNM, I’ve had 4 Capacity/Closed overrides. All 4 times, every student who attended class the first day got into the course. I’ve had 6 other classes where the instructor increased the course capacity significantly to allow all waitlisted students in. (The other 3 classes were French classes, which are not popular enough to fill.) However, overrides and course capacity increases will not help him with labs, as labs have no extra room for students.