HEC MiF vs MIM- Eurobros

My aim is to go into BB IB in London. Coming from a small European country with a relatively weak finance ecosystem, so my pre-master experience isn’t comparable to the German/Bocconi/LSE “Eurobro” profiles with 3–5 strong internships.

Profile:

2:1 GPA
675 GMAT
one very small/weak M&A boutique internship
one legitimate MM M&A internship, but at a firm/city with basically no London brand recognition
incoming Big 4 front-office role

Considering HEC MiF vs MiM for London high finance.

My concern with MiF is that recruiting starts immediately, so I’d effectively be competing with much stronger Eurobros using mostly my current CV + HEC brand. I’ve spoken to nationals from my country who did the MiF with limited prior experience and ended up in fairly weak/random outcomes, while candidates entering with stronger European brands seemed to do much better.

MiM gives me an extra gap year to potentially stack two much stronger internships before final recruiting, but likely delays FT by ~2 years.

So the question is basically:

Would you rather recruit immediately from HEC MiF and rely on Summers/OCs to build from there, or take the MiM and use the extra runway to stack stronger internships before recruiting for FT? (given id go into Majeure Finance in the M2, same classes as MiF)

How much do 1–2 additional strong internships actually move the needle once HEC is already on the CV?