Hi Scott!
Welcome to the forum! Thanks for providing a little background on where you're headed and what you are looking for in an MBA. If you are restricted by geography, you could do a lot worse than going after Ross. Personally, I think that program is fantastic and better than its ranking suggestions. If you're in Michigan and are already looking at an online degree, you may want to consider a part time program in Chicago (e.g. Kellogg or Booth). It's possible but it's a lot of time spent going back and forth. Something to consider though!
However, to your point about FT vs. PT, it really comes down to what you're using an MBA for. If you're staying where you are, then PT is generally ok. Or if funding is a huge concern. However, if you're looking to switch careers (like you are) then FT is the way to go. You get more experiences, the internship, and structure around the career search process. If FT is possible, I am a strong advocate for it. It isn't right for everyone but I think it would help you far more than a PT program.
To your second question about working during a PT or weekend program - yes. You can. Tons of folks do it every day and while it will be busy, it's designed to be do-able.
To your final point - engaging your recommenders is a little art and a little science. For example, you don't have to tell them your short and long term goals and, if you don't, you have to make sure they're prepped to not mention them at all. You don't want to have the issue where your essays say one thing and your recommender another. On the other hand, if your recommender really is a table pounder - be honest with them and soften the blow. If, however, you feel neither of these solutions are good ones, then don't reach out to them. Find substitutes that are equally impactful and explain it in the optional essay. But know this - you won't be the first person to ask an existing employer to endorse a career change, and you won't be the last!
I hope this helps and if you have any other questions - please let me know!
Bhavik