(includes TLDR) MBA vs non-business Masters for my situation (consulting, IBD, software engineering) Careers/Post Grad

Thanks for taking the time.

MAIN GIST OF QUESTION:

Can I do a MiF/MiM and still apply for Associate Strat Consulting or IBD because of my 3-4 years of experience? McKinsey Recruitment FAQ seems to imply that if you have 4 or more years of experience between undergrad and non-MBA Masters you can apply to Associate? How does that make sense when that way no one would pay for the 2x more costly MBAs

Background:

- UK based, Comp Sci BSc, ~ 3 years software dev in a Sales and Trading tech team at a BB bank. Don't want to do this for 40 years.

- Got an offer for tech Product Manager at a top 3 USA BB bank, which I will accept as it is the only thing (without further education) I can change to that makes me more commercial / "businessy". I did get a McKinsey Digital Strategy interview but was first case and failed.

- I want to possibly switch to strategy consulting or a finance (IBD or some other finance advisory).

- Problem: Since I want to do real business strategy consulting (and not some trap in Accenture or tech consulting), I really cant get much outside McKinsey/BCG Digital Strategy interviews (Bain, Big 4 Strategy Houses or Tier 2 like OW, LEK etc, and IBDs) since they all recruit like this:

Grad scheme -> Too out of uni for that

Free-floating Analyst/Associate -> No relevant experience (since software dev) and people with stepping stone jobs (like Big 4 Transactional Services/ Corporate banking for IBD) are a much better fit.

And I can't recruit for all stepping stone jobs at the same time.

- Hoping to better my background with MBA or non-Business Masters but a bit confused:

MBA:

- Good for Strat Consulting and IBD on Associate recruiting (where my background before won't matter much?)

- Good for better tech PM brands (Google etc) or VC (if I do a bit of PM)

Masters in Finance / Masters in Management:

- MUCH MUCH cheaper (even when assuming top brands)

- If I throw away my 3-4 years of software dev (irrelevant) experience upon entry I can do entry level IBD/Strategy Consulting applications

- Confusion arises from wondering if I can do a MiF/MiM and still apply for Associate Strat Consulting or IBD because of my experience? McKinsey Recruitment FAQ seems to imply that if you have 4 or more years of experience between undergrad and non-MBA Masters you can apply to Associate? Then, it is easier to do MiM/MiF and pay half the cost... must be a catch.

Thanks.