London undergrad to St Gallen - IB opportunities in Zurich?

I’m looking ultimately to move into finance in Zurich, Switzerland (either IB/AM/PE) and have listed some basic info on myself and my goal below.

• currently penultimate-year student studying at a target in London (LSE/UCL)
• incoming summer analyst at an EB
• will be able to get a SA M&A role next year in BB/EB (reapplying because intention to do a masters)
• hoping to do an MBF @ St Gallen and get internship / analyst position in Zurich (St Gallen known to be the main target for finance recruiting in Zurich)
• I speak German to conversational level but will be business proficient in the next year
• the choice to pursue a career in Zurich is personal and not really career-related

Ideally I want to work in IB (M&A) and I know a few banks have good teams there (UBS, JP, HL, amongst others), although also would recruit for PE (Partners Group is HQ’d in Zug, for example) and AM (BlackRock).

Assuming all goes to plan as I mentioned above, how viable does the Zurich scene look? This is really something I am motivated to do and I am a strong believer in “where there’s a will there’s a way” but obviously have to know all the facts before I go all in. Worst case, I can recruit for London roles after my MBF. Any advice would be really appreciated