Let me first qualify my comments by saying that while I work in a hospital, I am a nursing student with a little under a year left, so I don't have the direct experience with the nursing market that many of the contributors to this thread can offer. BUT- I've been a situation that sounds awfully familiar. Lots of experienced folks staying in the biz, very competitive markets with a lot of newcomers desperate to get in the mix, and I've used some strategies that, for me, worked very well. I know how bad it sucks to be a full time applicant, so maybe it will be helpful in the nursing arena.
I was a teacher for years (recent years
before I got into nursing school. Yes, you have to fill out the required on-line app. Yes, they ask you to upload resumes, licenses, etc. However, all that "required" submission only makes you searchable, not get any special attention. Another drop in a big, big ocean.
I tried some different things when I wasn't getting anywhere. It can be very difficult to get past the gatekeeper secretary, and sometimes, near impossible because of the instructions given by the boss. So, I went with a PRINTED resume, in a sealed manila envelope, to speak with the principal. Often, if i did a little legwork, I knew their name, and sometime's the secretaries, when i walked in. they meet a lot of people and might be nice out of sheer worry that they SHOULD know you. Never know.
At the very least, I could say, "that's ok- i understand your busy getting ready for the new school year, so I'll just drop this in her box and touch base at a more convenient time." If you can see the office/inbox and it's in a public access hall, just go like you know what you're doing. I've had them take it and say they would get it to them, but only sometimes.
Sometimes the secretary would take it/filter it anyway, but sometimes, they would let me put it in her office door box. It's harder to throw out a hard copy without even looking at it than it is to delete an e-mail. Then, I would follow up in a way that I asked a question in the e-mail, in order to provoke a response if only out of courtesy. and i always went AFTER i'd done all the "required" submission, and noted that they could review this at the end of my letter. This avoids the "please apply online, best of luck" dismiss.
did I get every job i went for? nope. but every job but one that i landed, i did. and it took some days, and some paper, and some organizing of names BUT, if i did 500 online resumes, and got 1 or 2 bites, i got 1 or 2 of every 10-20 "cold calls" i did. This includes my first hospital job- with ZERO health care experience and a RN school acceptance letter. For an unposted position that she just hadn't had time to put thru the system yet.
Maybe I'm totally off-base here and it's not like the situation you face. But it can't hurt! Will you still get no's? I'd imagine. Will you have people be surprised or flustered since you're not "doing it by the book"? I sure did. But bosses meet lots of people, all day long. Be one of them! Go after it completely prepared to push it just to the point that i could come back again later without being thrown out. Sell it like you work on commission- I may have rubbed a few people the wrong way, but I've never been asked to leave, and gotten several on-the-spot meetings, interviews, and jobs this way.
In the meantime, go to CE stuff- hospitals often offer them to non-employees. Go to professional org meetings. Get a non RN hospital job. ANYTHING to get you face time.
Professional assertiveness, when a decision maker sees it,has not often gone badly for me. I figure if I'm already at a "no" (job, that is), what do I have to lose?
BEST of luck. If you find something that works, pleases share! I'll take any "in" I can get