A couple of thoughts...
With your early age of problems with your BAV, and your coarctation, you are probably not a good candidate for a Ross Procedure.
Sounds like you may be able to push back the surgery some. In most circumstances, an MRI trumps an echo. If the results aren't consistent, I would insist your cardio get you in for a TEE or a cardiac cath to verify, if he insists you need surgery right away.
My personal take is that when you do go in for surgery, you should insist on having the coarctation taken care of during that surgery, and insist on being sure of and correcting any possible aortic aneurysms as well. "Well, it doesn't look bad enough to do anything with it yet" is usually followed six months later by, "You're going to need surgery again, very soon." Frequently, disturbing one part exacerbates any problems with the other parts of the system.
As to your valve choice, there have been a couple of people who've opted for a tissue valve at a young age, just to sew some more wild oats. The results have been mixed. While I like tissue valves, since you've already had surgery, and may need more for your aorta, I would think it best for you to avoid any extra surgeries that you can. That means carbon (mechanical).
It's not likely at your age that you'll get anything like twenty years on a tissue valve. Ten is likely far closer to reality. You'd have to be extremely strongly motivated for a tissue valve to be a reasonable choice for you.
Best wishes,