Well, I found a BRAND NEW in the box True GDM-12 for sale locally for $800. A bit more than I was planning on spending, but a bargain on a fridge that goes for $1300. Unfortunately the interior dimensions are 21 ½” W x 18 13/32” D x 48 15/16” H (44 7/16” to evaporator).
Morebeer's 14 gallon conical is listed as 19 inches in diameter and Blichman's is 18 1/2". Blichman also recommends an inch of clearance, although I'm not sure why you need it, quite frankly. 3/32nd's is not much, I'm wondering if the back panel would flex enough to fit it in.