In my meandering around the net, I discovered that the State of Florida has a shape file (or set of files) that define the PLSS for Florida. I see that JOSM has a plugin (OpenData) that supports shape files.
I have no intention or desire to upload that to the OSM repository. It is possible to load that into a JOSM layer, to obtain various corner points and shapes ? (obviously without loading into the main editing layer)
The idea to use external data in JOSM is first to download some data in the area of interest, then open the external data in another layer. I don’t know if the plugin supports opening the data in new layer though.
Some variation of OGR2OSM http://wiki.openstreetmap.org/wiki/Ogr2osm should do a raw conversion. Then in JOSM this file can be opened after first downloading data in the area of interest.