I apologize in adavance if I'm looking at this from the wrong angle. It sounds like the main problem is that you don't have a path to a green card, so you need to keep working indefinitely on your H1B visa. Am I understanding correctly?
If so:
1. What does your immigration attorney say about how to get a green card? Is it a possibility?
2. Is the MBA designed to ensure you remain employed, or to help find more fulfilling work?
I focus on the questions above because it seems like your finances are well in hand, assuming you do retain your employment.
1. My green card is already in process. It will come but it will take it's own sweet time. There's nothing I can do about it.
2. MBA for more fulfilling work.
I guess part of the reason I thought about an MBA is also kind of tied to my green card. My employer told me on my face that since I have a green card dependency, I should not be expecting big raises or promotions as long as I am here. I don't know if they can do that legally as I have no documentation. So it causing me immense stress in my personal life and I want to keep myself engaged and at the same time improve my career prospects in whichever way I can. Yes, I could change employers but I have to start my green card processing again and it sill set me back another year and no guarantees that my new employer wouldn't treat me the same.
You might sense that my posts are chaotic, which they are. But there's a lot of things going on due my employer and my green card situation. I apologize if this is too much of personal information to share.
My friend, that sounds like exactly the key information to share!
I have a dear friend (ex fiancee) who recently obtained full fledged US citizenship after a grueling 10 year process with many ups and downs, including a period of no green card followed by a green card. I deeply wish for your success in this matter.
I don't know the H1B specifics, so of course I assume you have shared these details with your lawyer to get their opinion. I know that can be expensive, but I don't like any situation where someone seeks unfair advantage.
Knowing several immigrants in varied visa situations, I am well aware that some employers do seek advantage. However, in some of those cases, the immigrant had power in the situation but didn't realize it. That is why I urge you to get lawyer advice about what leverage the employer has!
If you already have and your lawyer said switching employers would delay you, I'd consider staying where you are except for one thing. When my own employer didn't promote me and gave a reason, the reason they gave wasn't the real reason. It was just the reason that they could safely say. Later, I realized some of the various subtle problems I caused that were holding me back...later, meaning after those same issues got me instructed to resign, complete with a small buyout package to ensure no legal problems for the employer.
Due to the above paragraph, and the posts upthread saying that lack of an MBA shouldn't be a barrier, I suggest not getting the MBA on this employer's behalf. Based on how long it would set back your FIRE, I think I'd just keep the money in the bank, but do a lot of networking and personal self-development to prepare other options in case I did need to switch employers later.
My friend had no idea when her citizenship would come through until the last couple of months. I hope that your green card comes through soon.