Try Cranes' Kid Finish Stationery. Beading sounds like a sizing problem to me.

I coat with a rod but tape the paper taut to a sheet of 1/4" thick plate glass before coating. Three or four sweeps of the rod are made before the paper begins to buckle. Buckling and not starting with enough fluid tend to cause uneven coatings IME. I always dry the first coat and then apply a second to even out the emulsion layer and intensify the maximum density.

Your exposures sound about 4-8x what I would expect for a sunny day with conventional cyanotype formula. Mine usually print outdoors in sun between 7-15 minutes (in Michigan). Are your negatives excessively dense? Perhaps the pale color is partially due to underexposure through dense negatives. Do you print until the shadows have solarized?

Is your water alkaline? Try using a small amount of stop bath , vinegar, or citric acid in the rinse water. This may help you retain a stronger blue color and prevent bleaching and pale blues caused by alkaline rinse waters.

I usually have very intense blues with the peroxide treatment and double-coating. I've never tried the dichromate treatment but will do so soon.