I am sorry but a lot of red flags here. Your son should have known which courses to take for a transfer. Is there a particular reason he did not follow that pre-engineering path? Coops and work study sound really great but that will be a drop in the bucket. If he needs another two years worth of coursework to gain entry into a state school then it is likely that he will need to take just as many courses at an ABET accredited engineering school. What you do not want is for him to spend $60K a year in a college that will let him in because you can pay and then change majors. Look I do not want to come across sounding like an a-hole but how about tell your son to take some more classes at the community college to prove he can do the coursework in engineering and have HIM pay for it while commuting from home?
The stats you posted are decent if he can boost his SAT/ACT. Repeat after me: AUTOMERIT at schools that offer automerit.
Good luck!