Incoming GS IB Analyst with ambitions in USA PE

Keeping this vague to protect my anonymity.

I'm an incoming analyst in GS outside of the US and hold American citizenship. My ambition since finishing uni has been to make it to MF PE, but the options in my country are a little lacklustre as there are few MFs here and they tend to do deals infrequently. As such, I've been thinking of returning to the US to pursue PE there.

GS has a really strong internal mobility program once you hit the 2.5 year mark, though I imagine by this point I'll have missed the traditional on-cycle window.

Here are some alternatives I've considered:

1. Transfer into coverage and try off-cycle: I could try to transfer into a strong coverage group in NYC and cross my fingers for off-cycle.

2. Transfer into a PE adjacent group within GS in NYC: I'm pretty sure MBD has a PE arm, and I could try that and consider lateraling to MF if I still want to.

3. Recruit for PE here and move within that fund: I've heard that global mobility within MFs isn't great, so maybe this isn't the best option.

4. Try to do on-cycle and/or off-cycle from overseas. This seems like the least effective option since I doubt headhunters will want to take a chance on someone on the other side of the world, but doesn't require the same type of investment I suppose.

What would your advice be?