sorry to hear you are paying OOS fees at a UC. (I spend a lot of time on cc trying to discourage such behavior. Excellent school, but poor value at $60k/yr IMO. And Marine Bio is not their thing.)
Anyway, there are several issues at play here. In the first place, your S is still a newbie with regards to education. A Soph has barely gotten thru some of the intro science classes, and without the basics, its really hard to offer any value to a Prof (other than bottle washer.) I have no doubt that your son would be a hard worker and is willing to learn, but that’s just not the way research slots go. Second, a big public like UCLA has literally thousands of undergrads chasing those coveted research slots, so the competition for them is brutal. Priority goes to Majors who have already completed a STEM curriculum (and organic chem).
Does your S have a quant background? Advanced stats? Can he take a class/self-teach ‘R’? If so, he would be attractive to help others by running analyses of their research. Social science labs would love such help, but I would think that some Bio types would as well. The problem is that UCLA has a small Marine Bio program. (Most of their bio majors are premed and brutally competitive.)
I also agree with the transfer idea. Why not to a school that has a strong Marine Bio major, such as U-Miami. Miami’s marine bio program is 5x the size of UCLA’s even tho the school is much smaller. (If he applied as a Frosh, he would have received a nice merit scholly from Miami.) Heck, even UCSD’s Marine Bio program is 6x larger than UCLA’s.
For OOS money, I suggest that you to consider a mid-sized private school.
Good luck.