Hi Ben - Chad here from Moz. Kudos to Joy and Nigel for the great tool suggestions. I checked those out myself!
You make a good call out that there is no perfect method for tracking rankings given proximity and geographic location - I'd also add personalization as the other big factor. I was recently in the same room with 4-5 members of my client's digital team in Texas. We all ran the same keyword search on laptops and mobiles, and nearly all saw variations in the local results. So, there's that. : )
Moz has put a ton of thought and testing into how to get the most directionally accurate results, but personalization in particular challenges any method. It may go without saying, but I tell my clients to pick one method or tracker (maybe two at the most) then look at the directional changes in rankings vs. the absolute rankings themselves. It takes the pressure off small changes in rankings and allows them to become a useful confirmation that all is well or an alerting system that something has gone/is going in the wrong direction. This is in contrast to metrics like traffic (online and off), GMB insights data, and conversions/sales that tend be better indicators of success in your digital efforts. Best of luck! -Chad