I agree about the Home Depot mini-blind idea for affordability, but I would special order micro-mini blinds to the exact size you need.  They are much thinner so they will fit in the provided space much better.
I have not gone shopping for blinds in a while, but last I looked nobody stocked micro-mini blinds.  I wish the industry would bring back the micro-minis as a stock item because it's getting near time to replace the 27 year old micro-minis in our brick and mortar house.  I bought ours from Builder's Square in 1989 for under $5 a blind.  Because of the deal, I did have to cut them myself with my table saw which worked great.  We love the look and fit of the micro-mini much more than the standard mini blinds.