We just hired 12 new grads in my ICU. No experience necessary... but my god, hiring somebody with experience would be nice for a change.
Best strategy: apply, apply, apply... apply to all of the ICU jobs you can find and keep applying. All I applied to during nursing school was ICU jobs, and I had one secured about three weeks before I graduated, contingent on graduating and passing NCLEX. It happened to be 400 miles away from where I was attending school, and I probably could have stuck it out and found a job closer to me, but I preferred having the security of going to work immediately over waiting for a chance close by.
You might have a disadvantage with your current location. I see it would be difficult for you to relocate, so you should probably apply to non-ICU jobs, too.