STEM student lost in London IB recruiting

I think it's pretty funny that you've received such hilariously bad advice so far. Most people will say they're willing to help others but aren't necessarily interested in telling people the truth. Or simply don't know/refuse to acknowledge it. That's evident in your story and that's evident in my experience. 

What's the truth?

1. Being at a target is not enough. It is practically table stakes for IB internships. I say practically, not literally btw.
2. Big 4 audit spring is helpful, sure. Is it enough? If you're lucky perhaps. It's not anything like a sure win.
3. Fact is your CV rn is big 4 audit spring + target. Meh. Apparently 0 other evidence of finance interest. I (your imaginary hiring manager) has a bunch of CVs on my desks of people with IB springs. People who (through Nepo or otherwise) have interned in an actual finance firm. People who are actual contributors and persons of responsibility in the key societies at their unis (ideally finance related but not necessarily), have done relevant competitions, and are taking a demonstrated active interest in finance. And out of those people I probably still reject >50% of them. Why do you, who has done essentially fuck all compared to them, get to have the same opportunity? This is the Q you need to ask. I've just given you a bunch of clues as to the gap between you and the top candidates. If you're smart you'll close it.
4. Most people reviewing CVs (the document) give it a cursory glance, look for obvious red flags and say "probably fine". Most people aren't nearly detailed enough. If I'm really honest to have an actual half decent CV review, you need to spray and pray and get lucky, pay someone (anyone who actually knows what they're talking about probably isn't cheap considering you're basically paying someone a marginal banking wage or more to review it), or get lucky with a trusted family/friend in the industry who happens to also know what they're talking about. Your CV is probably "fine" . I've seen what gets through HR's screens. But would you like to leave your CV to being "fine" and getting lucky that the HR person isn't in a bad mood or a stickler, or would you like to have something undeniable (or at least as close to it with the experience you have)
5. In fairness to you, you have actually tried stuff. Networking (which doesn't matter in UK btw, you should know this if you've done research because every thread on it says the same thing), great effort. Emailing boutiques, great. You've had no results? Not great. Wanna know why? You're doing it wrong or not enough. That's really the only conclusion. Because other people do it and other people get success. There are definitely a lot of nepo out there but there are also others who are not that.

Sidenote: What is a JPM insight day? I've never heard of such a thing. Are you sure you were even eligible?

I just realised my writing style is really AI-like but I promise I wrote that by hand haha.