Any advice on breaking into IB from horrendously convoluted route appreciated

Hello fellow humans,

I've recently admitted to myself that i am very money and prestige orientated. I'm willing to work my balls off to get that lucrative job in investment banking. However my background is fairly ordinary. ABB at A level in sciences. 2.1 in Chemistry from York and Merit in International Business MSc from Nottingham (that's like the equivalent of GPA 3.3-3.6 from two Top 20 unis). I then ****ed around in a SME for two years in the chemical industry before taking a huge tangent and deciding to try out for medical school and working as health care assistant for 6 months to gain experience.

At this point I reckon i am 3-4 years behind my fellow applicants in terms of work experience as well as having mediocre grades. What would be a good way to proceed? I was thinking of maybe taking a convoluted route by becoming a CA in either Big 4 or Tier 2 accountancy firm and then moving into TAS to try gain some experience. At this point then proceeding to test the water with some boutique firms, as bulge bracket is obviously out of the question now, and if i get no bites then doing an MBA. May try and knock out CFA level 1/2 whilst studying for CA if i can. Is this a horrendous idea?? Your advice is most appreciated lovely people.