Regarding your question about exposure times for direct sun exposures vrs. in camera exposures - remember that exposures with negatives and the sun is using extremely bright (lots of UV) light through the negative to the cyanotype sensitized paper. The cyanotype emulsion is rrrrreeeeeaaaaalllllyyyyy slow compared to normal photographic paper. That's why you can't realistically use an enlarger to do Cyanotypes. Your exposure time would go way up because the brigthness of the light in the enlarger is so much less than the sun and way less of the right type of light. What you are suggesting by using in camera cyanotype sensitized paper is shooting an image of reflected light not direct light. At least by shooting in camera cyanotypes outdoors, you would have a chance to get good images, but you are relying on reflected UV light which would be much less than direct UV light.

Regarding the New method by Mike Ware - your cyanotypes will be a little darker blue which is good, but the formula is much more finicky with papers and you have to get the right paper/chemical match to get images without blothes.