My child is on Medicaid in home state but needs out of state insurance for college

My child is currently on Medicaid in Ohio but needs insurance for college in NY. I see 3 options:

1. Take the Gallagher student healthcare from the school for $3.3K annually. That feels like a lot, but I think she could still stay on Medicaid at her permanent residence in Ohio.

2. Apply for coverage thru the ACA marketplace and compare it to the cost of the school plan. With this option it is unclear whether she could stay on Medicaid in Ohio.

3. Become a permanent resident in NY and apply for Medicaid there. Obviously, losing Medicaid in Ohio.

Any thoughts would be appreciated, but I guess the most pressing question is whether she could be on an ACA plan as a student in NY while keeping Medicaid in Ohio.

EDIT: One other option that I didn’t originally think of. My partner has employer based insurance that apparently covers fully across state lines. It looks like our daughter could be added to that. Still working things out but I’m guessing that will be cheaper than the $3.3k.

UPDATE: I asked the school if there were scholarships for low income students to cover the cost of the school healthcare insurance. To my surprise, yes there is! They have a grant to cover the cost of my kid’s healthcare entirely! I wish I knew that before going thru all this lol. But so thankful!