Yeah, technically they ask for step scores (I suspect for licensing purposes) but as in most things it life is it all about what you have done more recently. Some cardiac programs even asked for my MSPE - I'm not sure about that reasoning, but I provided it. ITE scores are important, but in general play less of a role than USMLEs for residency (likely because the fellowship applicant pool is much smaller).
Since the pool is smaller, other aspects become more important. The subspecialty societies are pretty close-knit group so LORs become much, much more important. Thankfully almost all of them have their yearly meetings in the middle of interview season, allowing for networking opportunities. I'd try to get at least some research experience (especially for the more competitive specialties - cardiac and pain) - it isn't terribly difficult to get a poster accepted at ASA or any subspecialty meeting (SCA, SPA, ASRA, SOCCA/SCCM) and most residencies will pay for you to go if you get accepted. Take advantage of that opportunity, if nothing else the meetings are in pretty fun places.