The asymmetry you mention is not noticeable to me and I would advise against any surgery to try to correct it. The same goes for the lips. Everyone has some degree of facial asymmetry. Yours is minimal and not worth having surgery for it.
You look like a great candidate for a facelift. I would recommend seeing a few surgeons to get an in-person opinion from plastic surgeons known for their facelifts. I suspect you will find a more positive response than during your last consultation.
Need examination, or at least photos, to better tell the problem in your case and offer treatment options. There are many factors that play in eye asymmetry.