If you have offered sizeable equity packages (and have a nice office (or cushy remote benefits) and decent modern tech stack) then even the most boring startups can attract the best - so what is your company doing?
These days, while compensation and equity are of course important, there are other things (e.g. get to work on a wide array of stuff, no "big company" crap, etc.) that are likely going to be the real drivers in being able to attract talent.
Also, TERMS of the stock grants also matter. For example, if the options can be held for 10 years after departure from the company, that would make them more valuable. For the first 1-5 hires it may not make a difference because they'd probably do an 83b and buy all their stock right away, but for the next 5-15 hires the Series A price may still mean they'd need to put several or tens of thousands into their options, which not everyone can do.
Startups could also attract talent by offering atypical work hours (not arriving during rush hour traffic would be nice) or many other things, but they typically aren't willing to do that... for whatever reason. I've personally offered to work at startups in the evening for about 50% of my hourly-equivalent rate for 20 hours per week (so 1/4 of a salary for 1/2 of an employee), and they've not been interested. Until companies are willing to be unconventional to attract talent, I say the cries of "talent shortage" are not genuine. If there was a shortage, they'd be willing to be more flexible than most of them are.
I don't know what your role is, but I can understand why they aren't interested. If you're only willing to work at off hours, remotely, then it's highly likely they could get someone as good or better, more cheaply, by getting remote offshore talent (I worked with some great offshore devs in Brazil and Eastern Europe, for example).
In other words, if you've eliminated any advantage you would bring to the company as a local or US-based developer (assuming you're in the US), then your salary comps are now global developer salaries, not California salaries or wherever else you may live.
Problem is the "big company" stuff you are mentioning is no longer limited to big companies. I see the unicorns of the world trying to act like big companies from mimicking org structures to leetcode puzzles in interviews to downlevelling (our Level N is Level N + k at BigCo X). All this while asking candidates to slog it out for 10+ years before their quantum money is worth something tangible. Equally BigCos for what they are worth are extremely alluring by ensuring one does not live perpetually on ramen and BigCos also do a lot of things so you can move around reasonably (sure not as fluidly). Additionally given BigCos (at least the one I am in) value diversity and collaboration a lot the "bigco"ness is getting more and more of a strawman argument!
What would be ideal for me is startups of say 5-10 folks with roughly similar skill levels (and hence equity) with a really decent shot at a successful exit in a 2-4 year time frame. Where do you find these that are happy with such an exit instead of trying to become a unicorn and not stop until they take over the world by any means necessary?
Aka, paper money, that you have less than 1% of getting. Even if startup doesn't go bust, things like liquidation preferences will screw people unless they're VC or founders.
Startup stock grants are exciting mostly to people new to the SV. If you've been here for a while, you know how badly cards are rigged against engineers.
For instance: only a fool would think that a $500k equity package, based on eg a 409a evaluation, is anything like a $500k equity grant at a FAANG. Because the latter is cash and the former is lottery tickets.
I highly recommend anyone working in startup world to learn more about how it works in details, and understand how their companies deal with it.
You can own 1% of company that's sold for $100M and get $0. And it's all perfectly legal.