Great thoughts, all.
In regards to the Americas, I would say that the model doesn't accurately represent what happened. The parts that are accurate would be that many of the american colonies had an attitude of starting new, there were many groups, interconnection between them was easier than communication back home, and the presence of natives often perceived as hostile gave a common enemy - which we all know is the fastest way to enforce group cohesiveness.
In regards to the Mormons, I would peg them at the second gen (maybe call them phases instead?): they are currently engaged in maintaining the cultural standards created by the first.
OTU-wise, the drive for colonisation is:
1st, opening up relocation sites for populations living on worlds hostile to human life, or are overcrowded.
2nd, ideology. Persecution, real or perceived, or cultural isolation from the mainstream gives easy common cause. It will also tear the group apart as deviations within the group continue. Providing a common cause other than defense from other cultures (talking memetically here, usually not physically) reduces that risk. Settling a low value world, usually hostile to human life (did the Mormons ever expect Utah to become economically valuable enough for others to settle? Probably not), provides a common cause of surviving local conditions.
3rd, Bleed off and usage of risk takers. Most people wouldn't give up familiar, sometimes uncomfortable, low-risk lives. For those that don't, being forced by circumstance to live such lives can cause active psychological discomfort - hence why most of them engage in high-risk behaviors. They also tend to pick up interesting and varied skills. Providing a productive high-risk outlet for those behaviors, that often uses their skills, is an excellent method of utilizing such people. While many would go to the military or the scouts, not all are suitable for those services - colonies provide another outlet.

In regards to those very low pop garden planets, I suppose the first question we have to ask is - how compatible are those worlds with human life? Any world will have its differences, and those can mean life or death to a new colony. Pop 1 isn't a family that scraped together the hundreds of thousands of credits required to go live on an empty world: it's a biosphere analysis team.
Pop 2 would be a medium term survivability test, or a terraforming crew. Or an enclave of isolationists.
Pop 3-4 is when the work of building the colonial infrastructure begins, turning "move to a foreign country where you have to shit in a trench" into "move to a new state, maybe buy a farm. But we have toilets!".
Pop 5-6 is a continuation of the trend, usually focusing on stepping up food production - the surplus gets shipped off.
Pop 7 is when the colony comes into its own, and can industrially support itself. This is also the magic number of balkanisation.
Pop 8+ is when the world has to focus on supporting itself, reducing food exports to minimal. What does come out is usually luxury food stuffs.
Pop 9-10 is when the colonial cycle starts up again in an attempt to reduce the population pressure on local resources. In regards to Pop 11+, they're usually shipping people off as fast as they can.

On a hilarious side note, I'm pretty sure the most common export of a high pop world is compost, made from both food waste and bio waste. If a potential garden world is nearby (good size, easily adjustable atmosphere and hydrosphere, just needs life or has very primitive life), dropping a few comets for primordial sludge and mixing in a few billion dtons of compost can be very effective.