why don't you make a paper negative, and then use THAT to make your cyanotype ?
it isn't hard at all to make a paper negative from one of your enlarged prints - you just make a good print with the enlarger ... then take an unexposed piece of photo paper, make it wet + squeegee it off so that it makes a nice tight bond with your (+)print emulsions. take the negative out of the enlarger ... and blast the light through the paper print --- you can make a test strip &C to see what your exposure will be &C ... and then make your print. my times with a cold light head - and i have been getting good exposure f9 at about 8 seconds with burning and dodging after that ..
once you get your exposure you develop in anything you want - i use dilute ansco130 with a little oxidized developer added ( about 500 cc/1/ ) but there is a school of thought that film developer might work better .... by the end of it, you'll get a nice paper-negative ...
your sun-time to make the cyanotype will be sort of long because the rays have to pass through the paper but it should work fine. if you use single weight paper that works great, but regular paper works fine too.
i'll be doing the same thing in a few weeks time