The "Rex" process uses some different chemicals as well as the two you mentioned, I think. (which are the two components of the "classic" cyanotype)
I looked in to it a while back and found it hard to track down the exact formula/process as the guy who "invented" it seemed to want to sell you a PDF with the information rather than make it public. presumably it's leaked out by now if you google hard enough.
as i recall you also need ferric oxalate and/or oxalic acid.
The problem you face with using an iron-based rather than silver-based process for lensed photography is that the former rather relies on UV for the process to work, while the latter doesn't, it relies on visible-spectrum light.
This matters because photographic lenses block most UV (presumably due to the type of glass used, as the ordinary window glass we use in our contact frames for cyanotypes doesn't cause a problem) and therefore the sensitised paper won't receive sufficient UV to get the photochemical reaction going that produces the image.
There are good reasons why Silver halides came to dominate chemical photography - the alternatives are few and very inferior. There may be industrial processes that offer equally good results (I think there's something based on diazo dyes been done?) but it sounds like you are after something you can do in your bathroom/kitchen.
If you can track down a much faster cyanotype process that doesn't rely on a rich UV source, maybe it'll work, but you might have to do the research & testing yourself to see if the "Rex" will do do what you want. You m ight also have a look for Mike Ware's "new cyanotype" process.
