Advice for getting into IB - EU/UK

Hi I'm 24 and work in a BB in Corporate Finance (MS/JPM/GS), getting promo to Associate in Jan but want to break into IB, thinking my best bet is to apply for MFin LSE/Bocconi/LBS/etc for strong IB placement. MSc would be '26 and I'd be age 27 by the time I start from Analyst again which I think is ok in EU but less common in US. Lateral move off the table, spoke to HR and VP said they'd look for deal exposure at associate/senior analyst. Graduated 2022 from a UK non-target. Couple questions:

Is there a better pathway? I'm thinking if I try network to MM/EB/etc it is much riskier and I'd be "waiting around" with slim chances
Will they comb through undergrad transcript or is it typically MSc they look at once at that level?

Thanks a lot if anyone sees this