
Just a couple of comments. First, I don't disagree with those of you who state the OP should use a contact printing frame  you have given good reasons such a holding the paper flat, avoiding newtons rings, etc.
However, I find it interesting that whenever someone posts some kind of mathematical derivation here, there a bunch of people who chime in saying "you're over thinking this". I just don't buy into this  there are actually some of us who enjoy carrying out a good derivation to see where it leads.
Jason, math does not break down when it hits the real world  it simply becomes more complicated. One of the truly remarkable things about this universe we live in is that it can in fact be very accurately described by relatively concise mathematical equations. Indeed, this leads into a great philosophical question. Is math something humans discover, or is it something we invent?
mfactor  I a COC of 0.022mm is smaller than you can detect no matter how close you get.
icracer  In your diagram, I see that you computed your COC for the special case of a point directly under the edge of the exit pupil. However, when you making a contact print  say 8x10, most of the image points will be further off to the side so you will no longer have right triangles to work with  I believe they will be obtuse triangles. Did you try computing the COC for these?