The XDA forums don't have anything listed for your device. You can still improve your privacy by disabling applications (or uninstalling them through Universal Android Debloater) and replacing them with FOSS alternatives where possible. If you don't already use F-Droid and Aurora Store (or equivalents), switching to those app stores instead of using the Play Store for everything will help you to change your app drawer over time. Take note of Aurora Store's privacy report section that lists known trackers bundled with applications, it's a very useful feature that is often overlooked.

Could you find something used but supported by Lineage OS? Maybe you could get a older phone and then sell your current device.

A old worn phone shouldn't be super expensive. For instance I can find my current device (moto g7 power which I bought new in 2019) for around $50-$70 used on eBay. There are plenty of used devices that can be had for less than 100.

Appreciate the help, guys! Sucks that my model isn't supported, but maybe I'll end up with a new phone at some point (hopefully before this one dies).

If you do end up having to wait until you get a new phone, you could disable Google Play Services and the Google Play Store, and that would help quite a bit.

look on XDA developers forum for your model. They usually have plenty of alternative ROMs

There is a device compatibility page on the /e/OS website (we are on /e/ almost family-wide here); I see plenty of 'Moto G' but I don't know enough details on your model... /e/OS is efficiently degoogled, with G. closed parts all replaced with open source equivalents...