Your post is very confusing. Perhaps explain your logic here:
So you could be a CS major at GMU, with just six more classes, which is at least another semester —and I’m not sure if you will keep your full time job, so more likely another full year of college.
But you’re considering instead taking eleven more classes (which will take at least another year, but more likely 18 months or longer if you keep working full time) just to be able to transfer to UVA or VT so that you can double major. It sounds like you can’t transfer in as a CS major, but you think you can transfer in as an engineering major, then just switch into the CS major.
Can I suggest that the simple option seems to be to go to GMU and get your degree. You appear to already have a strong resume. You must be aware that at your age, employers care far more about your work experience then where you got your undergrad degree. Your plan seems incredibly convoluted and time consuming.
Then you ask if Ivy League extension schools want you to apply as an engineer. Why? Extension programs just want you to apply for whatever you want to study, right?. I don’t understand why you’re applying to Ivy League schools at all when the extension programs afaik, aren’t known for CS or Engineering. Do they en offer ABET accredited programs? But you also want to apply to general studies programs at Columbia for reasons that are unclear. Living in NYC is very expensive.
“I figured I already spent so much time in college, why not go for the best ones at this point?” The best one, for you, is the college that gets you the degree you seek. Your work experience is of FAR more interest to employers than an Ivy League extension school degree. Take the path that offers you the most affordable degree in the least amount of time, using as many of the current credits that you already have.
I very much get the sense that you’re hanging on to a misguided idea that the Ivy League name is going to propel you into some kind of amazing job opportunity. It isn’t. The things you’ve already done seem to be serving you well. By all means, get a BSc in CS, but you’re already on a great path with your work experience. You don’t need to jump through hoops to finagle a degree from Columbia General Studies. I don’t think employers will care, tbh.