I have never dealt with Fluke service, but it is my understanding, that you have to call Fluke with the correct part number before they give you a quote. Since I can't find a 79 III service manual (yet), calling Fluke probably won't get very far.
The only ebay seller that might have it is USA based a-fluke and he doesn't ship Internationally.
As I'm also in Canada, finding a dead Fluke 79 III to scrounge for a lcd is not zero %, but close to it. While ebay offers more stuff to Canadians via the global shipping program, the odds of finding a 79 III for parts at a reasonable price considering taxes, custom/duties, exchange rate, etc, is not zero, but again close to it.
Fluke meters sold for parts can sometimes reach mind bending prices.
The Fluke 79 II glass was sold off by a seller who had no clue to what they were worth. He sold batches of 50 (fifty) starting at 99 cents. I alerted someone here and he has a lifetime supply of lcds for 99 cents + $10 shipping.
Pretty soon all the Fluke refurbishers/resellers caught on and bought them around $10 for 50 lcds and resold them for an outrageous $15 each or more. Sadly, many people bought them at $15 or more.