Need only slightly better reception. Will a different antenna help?

I read more than 30 post here before posting this question and didn't find any that seemed to address a scenario quite like ours.

We have a little plastic flat antenna (with an inline amplifier) we bought at the discount store for less than $20. It has served us well, but at our current rental house, we can't get steady, dependable reception for CBS (WCTV), the only reason we need an antenna at all. It will be fine for few minutes and the pixelate or drop out intermittently. When we want to watch CBS, we move the antenna out on our balcony railing and point it generally towards Thomasville (where the CBS station is broadcasting from). For context, when we turn off the amplifier, we get nothing at all. From our house, 62.3° is basically right into a tall stand of oaks. There's an opening in the trees more eastward though.

Would we benefit from a different indoor antenna? Should we get an old-school rabbit ears-style antenna? Given that we're able and willing to temporarily move the antenna outside for use when needed, does that open us up to a different style antenna?

Here's my RabbitEars report: https://www.rabbitears.info/s/2270086