When i first transitioned from E.R. to ICU, i asked to be cross-trained from the hospital i was currently working ER, to be able to float to ICU as needed. At the time, (long ago) the ICU was desperate enough for help, they agreed. I then floated, week by week, between ER and ICU, without losing the seniority i had acquired in that facility.
You also might consider applying to your hospital's acute-care float pool, and, after gaining experience and training in the multiple depts, if you do not love floating like i do, then, you could apply at next available ICU job, and the manager of ICU would already be familiar with you.
I myself don't completely understand why you'd have to change hospitals, to change units, but, it could be that your ER manager would not let you go to ICU, or would have discussion with HR or the ICU manager and discourage them from choosing you for the ICU position?