I applied for a research role at GWWC a few years ago (?2015 or so), and wasn't selected. I now do research at FHI.
In the interim I worked as a public health doctor. Although I think this helped me 'improve' in a variety of respects, 'levelling up for an EA research role' wasn't the purpose in mind: I was expecting to continue as a PH doctor rather than 'switching across' to EA research in the future; if I was offered the role at GWWC, I'm not sure whether I would have taken it.
There's a couple of points I'd want to emphasise.
1. Per Khorton, I think most of the most valuable roles (certainly in my 'field' but I suspect in many others, especially the more applied/concrete) will not be at 'avowedly EA organisations'. Thus, depending on what contributions you want to make, 'EA employment' may not be the best thing to aim for.
2. Pragmatically, 'avowedly EA organisation roles' (especially in research) tend oversubscribed and highly competitive. Thus (notwithstanding the above) this is ones primary target, it seems wise to have a career plan which does not rely on securing such a role (or at least have a backup).
3. Although there's a sense of ways one can build 'EA street cred' (or whatever), it's not clear these forms of 'EA career capital' are best even for employment at avowedly EA organisations. I'd guess my current role owes more to (e.g.) my medical and public health background than it does to my forum oeuvre (such as it is).