Regarding the mesh...back in the mid '70s there was a mural processing tube available comprising a clear plastic tube, end caps for the tube, and a fine mesh-like material (might have been a very open-structure foam). The paper (it was FB in those days - cut from a long roll, sold as mural paper) was rolled with the mesh into a tube small enough to fit into the processing tube. Chemistry was introduced via one of the removable end caps. Agitation was a combination (if I'm remembering correctly) of rolling on the floor and periodically tilting from end to end. I made quite a few prints this way (and I'm guessing again they were in the 30"x40" size, or there abouts).
Washing was the challenge. Repeated rolling and re-rolling in a tub of water, or deep darkroom sink, was what I used. Drying was clothes pins and flattening was under a weighted sheet of plywood.
I haven't looked for a mesh/foam like this system used, but some industry must have something like this that can be retasked.
Good Luck with the enlarger!