Deprecating network=US:NFSR:* and standardizing on network=US:USFS:primary seems good for National Forest Highways (trapezoid shields). These primary routes seem very similar to state or county routes and it makes sense to me that they would be mapped as route relations.
It’s not clear to me that route relations make sense for the lower maintenance roads that use smaller horizontal or vertical signage. These are all generally lower classifications like unclassified, service or track and seem much more akin to local roads than long distance routes. If every National Forest road is to have a relation, that would suggest that every named road and street elsewhere should too. This may eventually make sense given the one feature, one OSM element principle, but currently that is not standard practice. For now, I would suggest we just tag these lower maintenance roads right on the ways just as we do with lower classed municipal roads and streets, but eliminate the prefix from ref. network can also be tagged right on the ways to indicate vertical or horizontal signage.
I agree that network=US:USFS:secondary:low_maintenance feels a bit awkward, but I also don’t have a better idea for a network value. Alternatively, a new tag indicating signage style could be coined. Something like ref:sign_style or ref:shape including values like horizontal and vertical could work and would be similar to the existing ref:colour tag.