No chance. W&M is a public university supported in part by Virginia taxpayers. So yes, it caters to Virginia residents – 2/3 of admitted students are from Virginia and they get full calculated need met (with loans, in my son’s case). There is no commitment to meet full need for OOS students. There are a few scholarships that will provide OOS students with an amount equivalent to in-state tuition, but I don’t think transfers are eligible for those.
So you are considering paying OOS tuition in Virginia for four years to attend W&M for two – when you could attend a college in your home state for 1/3 to 1/4 the cost? And then go on to grad school? That is unwise, to put it mildly.
I think you need to go back and read some of the advice given in your 1/4/2016 thread. At this point you just need to focus your efforts on a school where you can finish your degree in the most cost-effective manner. Prove to yourself and others that you are capable of finishing a course of study, instead of dreaming about improbabilities. You don’t need a “TOP college” (your words) right now, you need one where you can get a marketable degree. So do well and save the elite status for grad school.
Just my $0.02
Also, W&M does not have an engineering major; they have a combined degree program with the engineering school at Columbia University.