Moving to another geography in PE

Hi everyone
I work for a UMM/MF at one of their offices outside of the US & Europe. I joined the fund as an intern straight out of college and was recently offered a full time analyst position. I have 1 year of experience.
I've always wanted to move to Europe (I hold a passport from an EU country) but now that I have this full time position I don't know if it's the right decision. I would like to work in PE if I move there
For starters, my PE firm doesn't allow transfers from my office to European or US offices so that's outside the table. I was thinking that I have some other options but I don't know if they realistic
1) Find a position at a PE/VC fund through a portal such as PER. This seems very challenging as I did my undergraduate degree in a non US/European university and I don't hold a masters. Is it still doable?
2) Work 2 years at my current fund and apply for a masters in finance at LBS/HEC/LSE and then recruit for PE. From what I've heard, most people graduating from these programs recruit for IB so I'm not sure if I would get what I want out of those programs. I definitely prefer to stay where I am rather than working in IB
3) Work 4 years and do an MBA. This is the most logical career path. However, I've heard from former associates from my office that took this path that i) US/European funds consider that associate experience in PE outside of developed markets is not valuable given market differences ii) Senior associate positions are rare in Europe and most spots are filled by people with return offers
What do you think? What would you do in my position? Any other ideas?