Johan, I am the anti-logarithmic force (or any Systems Engineer could help you through that problem).
It's all about how you manage and present "Attrition" in varying means.
- Mortality Rates aren't that difficult to code into the game. You were lucky, in this era, to live to a long adult life. Some regions, the average lifespan was only 29 years old!! So your current "lifespan" system is way off the mark compared to historic norms (I'm seeing tribal leaders who consistently live into their 70s without fail, statistically impossible in this era - tribal systems should have an even lower Mortality Rate, especially Nomadic types). Simply put more "normalcy" into the game, to include real Mortality Rate statistics, and you already have a start for a good, representative and somewhat "real" attrition system.
- Families bore 4-6 children in the face of these low Mortality Rates. So the "lucky ones" made it to adulthood and made it into power. Let's see that play out. You're throttling back the rate of child-bearing due to a data problem in either design and/or your Game Engine. Seems like Design and/or Game Engine improvement efforts need to get busy to "Save the Children."
- Disease could be used as yet another factor in culling the Families (and Pops). In CK2, you used Disease wandering around the map to cull children and adults. You already had another game that faced this problem and handled it well.
- And this is a "Short List" that could be expanded into upwards of 100 or more metrics and events that help keep the population "manageable" in I:R or any other Paradox Game. It's just a matter of bringing together good Design work with a tight Systems Engineering approach that has a well-oiled machine (Game Engine) to perform the heavy lifting work.
- I think this topic is also on the edge of the data/engine problems for your limitations on Provinces in a game. At some point, Paradox needs to get serious about improvements (if not already) in underlying systems, foundational work. I would assume that is ongoing, but the Player Community probably isn't well informed as to how these issues that limit design and more expansive gameplay, are being handled behind closed doors at Paradox.