What a neat idea! I really like your tiles a lot. I have thought of doing something along that line but so far...well, its still on "the list" lol. And the "having no purpose but to lay around being pretty" must be common...in my case its beads :) Can't say what is so fascinating about them but I just love to have them. I have actually made necklaces out of a few but designing jewelry is not my forte, sadly. I copy others pretty good though!
If you do get around to finishing your door project you simply must share with us!!!