Some interesting ideas here.
A couple of things to throw in, that you might want to consider how they impact the analyis...
1. A lot of this is discussing how the sawtooths serve a person who only wants to play on one difficulty level - how long would they have to wait for that difficulty. But are there many people like that? I'm guessing (based only on general impression) that most people would have a range of difficulties that they are happy with, eg. a person might see themselves as a monarch player, and therefore be happy to play prince, monarch or emperor, and be willing to have a go at levels outside that range (especially since an easy or hard map can often make a difference at least equivalent to one difficulty level).
2. I also imagine that few people come to the competition looking to play a game within eg. 1-and-a-half months; I'm guessing many more people come here wanting to play something *now* and so will be choosing from what's available *now*. I suspect that separate sawtooths may serve those kinds of people better because they make it more likely that the games available *now* will be of widely differing difficulties, whereas with one combined sawtooth, you're more likely to see something like games available *now* being noble, prince, and monarch.
3. It's probably worth pointing out that the three sawtooths we currently have aren't really independent in practice. There's always an element when setting a game of looking at what other games are currently available and adjusting the sawtooth accordingly, eg. as a few months ago when I skipped the deity BOTM, or this month Ainwood sped up the GOTM sawtooth by going from warlord straight to prince.
A couple of things to throw in, that you might want to consider how they impact the analyis...
1. A lot of this is discussing how the sawtooths serve a person who only wants to play on one difficulty level - how long would they have to wait for that difficulty. But are there many people like that? I'm guessing (based only on general impression) that most people would have a range of difficulties that they are happy with, eg. a person might see themselves as a monarch player, and therefore be happy to play prince, monarch or emperor, and be willing to have a go at levels outside that range (especially since an easy or hard map can often make a difference at least equivalent to one difficulty level).
2. I also imagine that few people come to the competition looking to play a game within eg. 1-and-a-half months; I'm guessing many more people come here wanting to play something *now* and so will be choosing from what's available *now*. I suspect that separate sawtooths may serve those kinds of people better because they make it more likely that the games available *now* will be of widely differing difficulties, whereas with one combined sawtooth, you're more likely to see something like games available *now* being noble, prince, and monarch.
3. It's probably worth pointing out that the three sawtooths we currently have aren't really independent in practice. There's always an element when setting a game of looking at what other games are currently available and adjusting the sawtooth accordingly, eg. as a few months ago when I skipped the deity BOTM, or this month Ainwood sped up the GOTM sawtooth by going from warlord straight to prince.
)
And I have no problem even if at a given month all three XOTMs are Deity - I just ignore them and go play the settler level HOF Gauntlet instead! 
