I think with your ability that you should pursue the Engineering degree. If you can find a way to work in the automotive area while not in class you can have the best of both worlds. A couple of the posts above mentioned checking with shops to see if you could help out and learn at the same time. I had to work while going to college but I chose the oilfied instead of automotive because it was readily available. The experience I got while working has been very valuable for me through the years even though it doesn't relate to my work at all. After college I went to a 9 mos. auto body school, completed that and started my shop. After a while I was offered a job in the Material Control area and I have just worked on cars as a hobby. It's been great.
WyoTech used to be a first rate school with an actual waiting list of employers who wanted graduates. Over time it has grown into just another expensive trade school. With a degree you've got a lot of options. Employers often look at a degree as a indicator that you were willing to commit and follow through more than the specific information learned so it is not uncommon to get a good job in a field other than your actual education. As previously mentioned, I can't imagine that an engineer who can actually weld or work with their hands would ever be out of work.
Good luck with your decision!