Hi,

Maytag MZD2766GES side by side refrigerator,
don't know the age

The serial # will help with that...
http://www.applianceaid.com/appliance_age.html

the ice seems to start at the back and each day
extends nearer the front. After 3 days it is almost to the door

Certainly sounds like the defrost drain is clogged or restricted.

Initial guess is that the defrost drain tube might be clogged, but
I this
beast does not seem to have such a thing

It does, behind the back wall in the freezer is where it starts.

http://www.applianceaid.com/frig_leaking.html
Some helps and tips.

There is no evaporation tray below the fridge

Yes there is...you can see a pic of it from below...
http://www.repairclinic.com/referral.asp?R=153&N=665946

jeff.
Appliance Repair Aid
http://www.applianceaid.com/