Adding cycleway=lane to existing highway

This involves node 128709371 (and likely a couple of adjoining nodes). Florida DoT has been doing a road improvement project, which is almost finished. As part of that, I noticed that a couple of turnout lanes (from the primary route) now have bike lane logos, but that these are not present along the majority of that highway. I queried the region 2 DoT office, and what they responded with is this …

To answer your question, yes, they are considered bicycle lanes. The outside strip of pavement, which we call the paved shoulder, is the best place for bicyclists on the roadway. The paved shoulder is also to have a space for motorists to safely pull off the road and to help protect the edge of the driving lane pavement from damage. The roadways are for all travelers not just motor vehicles. The markings are for motorists to know that bicycles may be in that space and to watch for them. We want all users of the roadway to be as safe as possible. The locations you named specifically have right turn lanes. The marked space is to allow bicycles to continue on the paved shoulder but to make motorists aware that they are crossing into the path of bicycles. Normally, we don’t mark the shoulder areas with the bicycle markings in rural areas, but in the case of right turn lanes we want the added safety.

So the response tells me that the pavement (beyond the outer lane marker) is both a cycleway=lane, and a shoulder for disabled vehicles. Since there are some bike lane markers, should this motorway be tagged as cycleway=lane ? Much of the motorway runs parallel to a dedicated rails-to-trail, so the motorway is probably not the preferred (i.e safest) route. Curious to hear what other think about this.

Maybe cycleway=shoulder as described on the wiki would be appropriate?