I applied at an ALF after being licensed as a CNA, and they wanted to hire me as a dietary aide with a secondary position as a CNA. They called it a "universal" position. Luckily the LTC facility I'm at now called me (it's the position I wanted anyway, as I did my clinicals there). A perk to being in LTC, at least in Wisconsin where I'm at, is that you can get a reimbursement of CNA course tuition/costs up to a certain amount but it has to be pretty soon after you complete the course and receive your state license. Just make sure you're meeting your state's requirements to maintain your license at this facility.
I wish you the best.