TLDR: if you can align the reads (i.e. if you have a reference genome) then you might want to filter on mapping quality, and not on read accuracy.
In NanoPlot, the mean read quality is the mean of the base call quality scores. To be entirely correct, those (Phred scale) base call quality scores are first converted to their probability of being correct, averaged, and then back to the Phred scale. A bit more about that can be found in this blog post.
ONT will by default filter on a minimal quality score of 7, but that's quite arbitrary. I don't know why they went with that score. For my applications, which is structural variant detection, I don't filter at all. If I get a low-quality read, which does map reliably, and identifies a variant then I'm happy. The quality scores match quite well with the percent identity if your data is recent at least. So as such, you can estimate the error rate of a read, based on the quality score. A quality score of 7 corresponds with a ~80% accurate reads, which is not amazing. See also the image below for how the Phred score corresponds to the probability of error or the accuracy:
For your application I would let the aligner judge reads: if it aligns with a high mapping quality to one of those genes, and not to the others, then that's a good thing right? I don't know how similar the genes are, and how long your reads, though, and also not what your aim is.