Ah! I'm sorry I missed "Surrey"!
And the same thing happens here... often in late afternoon the fog comes rolling in, and in the winter the tree shadows start early. Many times I've been out walking around in the yard with my contact frame, trying to find the last sunlight to finish off a print. And it doesn't work very well.. late in the day even if you can get direct sunlight, it's not very actinic. And for whatever reason, the prints made with the BLB bulbs seem to me to be "missing something".. I can't put my finger on it but they never look quite as good and it seems to be harder to control contrast "just right". I mostly use the BLB for testing and not much for making final prints. I don't know if that would be a problem with cyanotype.
With salt printing, there is a "developed out" version that be done even on cloudy days. I've never tried it and I don't know if there is something similar for cyanotype. Beside x-ray film or litho film or digital OHP... it does seem that oiled or waxed FB paper negatives might be a good thing to try. I'm having trouble imagining coating liquid light on vellum... it tends to curl when it gets wet and is not dimensionally stable, and the clearprint vellum has screen markings. Dura-lar or glass would probably work, but then it's not really a paper negative anymore, is it! And single weight paper isn't very common anymore, RC or FB. Good luck! Let us know how it goes if you try something!