We routinely leave our pool for 6 weeks in August/September. We'll in eastern PA, same weather as you in NY. We bring it to shock level the night before we leave and add polyquat 60 the next morning, then put the solar cover on. We don't have a winter cover or we'd use it. We turn the pump off.

Yes, it's green when we get back. Not a big deal. We dump in 3 large jugs (182 oz) of bleach the day we return and turn the pump on. After a couple of days of steady high concentrations of bleach the water is clean again, albeit cloudy. We keep the pump running, backwash/rinse the filter, might brush the bottom, and within 10 days the water is clear again.

Unless you can hire a pool service or someone to dump some bleach in and agitate it in the water (tough to do with a cover on) you may just have to accept you'll have a green pool. If you use BBB, that should not be an obstacle because a green pool is easy to fix.