Putting together the various other archetypes which people have suggested:
Xavi suggested the magical bloodline archetype: Having a student to pass on what you know. Similarly, humboldtscott suggested the passing on the legacy archetype. Both of these would probably use the same growth rates as my Wulfenbach: the apprentice is selected with great care, and taught demandingly but well.
ladyphoenix suggested the Ambition and Social Pressure archetypes. As she points out, different houses have apprentices for different reasons. Her Ambition and Tremere-style growth rates can probably be modelled using my Walder Frey archetype (multiple apprentices over time, taking care over each one); the Bonisagus one would use something closer to the Accessoriser, with an apprentice taken once one has some power, to show that you intend to pass it on. (The number below is an average of the two).
humboldtscott also mentioned the Grow the Covenant archetype, where a group of magi will all take apprentices at once. The way apprentices are looking pretty rare in my count right now, I would say that this might have been an archetype further back in history, but no longer - 4 or 5 suitable apprentices all being available, all at once, just when you want them, isn't really something that occurs in the modern age. Respectfully, humboldtscott, I'm going to leave this one out of my calculations for those reasons. I like it but I don't think it fits the world.
If we assume that all the archetypes
Abraham: 0.4
Accessoriser: 0.9
Ambition: 3
Apprentice Factory: 5.3
Atoner: 1
Doubler: 1.6
Magical Bloodline: 0.8
Passing the Legacy: 0.8
Social Pressure: 2
Walder Frey: 3
Wolverine: 0
Wulfenbach: 0.8
Assuming an equal split between all these archetypical parens types, this gives us an average of... 1.6. Which matches Chris's numbers very nicely.
Drum roll please. I think we have a solution.
With the number of roughly 60 million giving us 6,000 Gifted, it would appear that 1 in 5 Gifted are Hermetic. Which suggests that Intelligence and The Gift correlate extremely strongly, since there's no way that 1 in 5 people have a maxed-out Int if it's normally distributed. Even if we assume that Hermetics are twice as common because they live, on average, far longer than other Gifted traditions, that's still only 1 in 10.
To be honest, that fits my growing perception of the Order as having already maximised in size, and already having the mechanism for locating and acquiring every suitable apprentice in Christendom. It's nice when all the data points in the same direction.
Something else I wanted to mention - Xavi, Chris and I all work on numbers which assume that the Schism War was apocalyptic in proportion. 40-50% population loss would probably result in something like 20% of all covenants being abandoned, and the surviving ones being depopulated significantly. Lots of wonderful, slightly glowing ruins lying around, many of which would not have been repopulated (nobody knows they're there, or nobody wants to go there).