I made a transition a little over a year ago. Before that, I interviewed with a company in downtown Chicago called Wellspring, a division of Huron consulting, maybe a year and a half ago. At the time, the position consisted entirely of appraising Healthcare facilities. The downside was that out of town travel was required on a weekly basis. I was torn over that position and eventually turned it down because of the combination of downtown location and travel (I am a father of four). I thought very highly of the MAI who was going to hire me, made the decision very tough, but was less comfortable with the Finance guy he reported to.
Taking classes and keeping your current position (outside of real estate appraisal) might be difficult if you take courses from the leader, the Appraisal Institute. The first course most beginning appraisers would take is Real Estate Appraisal Principles, but it is only offered as an all day class which goes four days in a row. Possibly other providers would offer evening or weekend classes.
Another option...
Take an online class from the AI that might show your interest in the profession and then include it on your resume. Second, talk to some appraisers about the types of property you would like to appraise. Third, take an entry level position with a commercial appraiser or firm, who might be more sympathetic to the class schedules. The advantage is you will gain commercial experience much faster jumping in full time. The downside is you would likely face a decrease in pay, depending on the type of firm. I don't have knowledge of what the larger firms pay, but the smaller MAI offices were on the low side starting out, but I think its fair considering what they invest. The upside of that is the potential earning after two to three years can jump.
I don't think this option is better, just a different way to go.
Let us know how your story turns out.