An anonymous commenter asked which of the sheep’s 4 stomachs is used for haggis. He thought it was the omasum. I had no idea. Research is amazingly tricky here. My knowledge of sheep stomachs is growing exponentially but not all of it tells me what I want to know. The general word (including Alan Davidson) is that it’s “the big stomach” that's used, though you can obviously find online dissenters. There's a commercially available "Lamb's Traditional Haggis" which claims to use "the smaller stomach," whatever that might mean. Here’s an anatomical diagram.
That image comes from this website:
There you will also find this handy chart:
Capacities of digestive tract of mature sheep
1.2 to 2.0 quarts
5.0 to 10.0 gallons
0.5 to 1.0 quarts
2.0 to 3.0 gallons
2.0 to 2.5 gallons (80 ft)
1.5 to 2.0 quarts
The site tells us that the reticulum is honeycombed, so I think we can definitely rule that one out.
So it appears the rumen is the most likely. It’s certainly the biggest stomach, though a ten gallon haggis would be a fearsome object and I certainly don't think I've ever seen one that big, though I'd definitely like to.