They follow the factor method with factors n, 2 (for 2n lanes). The first and last stage consist of two n-n flow routers each, one in the left-lane world, and one in the right-lane world. The middle stage consists of n virtual 2-2 FRs*, but needs extra splitters for the sideloading, which is needed to move items form the left-lane to the right-lane world and vice versa.
What I find more interesting though, is that they were already lane flow routers before I made the first and last stage FRs - this means that for at least some of the FRs made using @Scarab's construction method, the FRs of the first and last can be replaced by (TL) balancers, potentially saving on splitters. I'm pretty sure this substitution will be allowed for FRs factored as 2×n, but looking at @Scarab's book I couldn't find FRs where this would save splitters, but it could at least make it easier to save space.
*They are not 2-2 LFRs because I needed 4 physical splitters to make my earlier 2-2 LFR, 2 splitters were not enough. I call them virtual 2-2 FRs because the splitter networks for them are the equivalent to that of a 2-2 FR (splitter networks don't care about lanes).
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Re: Factorio-SAT
I also realized that Factorio-SAT doesn't need to handle priorities for it to work on FRs, as it only shuffles splitters and belts around, so you only need to keep track of which splitters need which priorities, so once you decide on a topology, you could pass it to Factorio-SAT to make a compact blueprint. But I don't quite know how to write the topology in a way that Factorio-SAT needs it, and it won't work for LFRs since they use sideloading.
Note that the sub-FR -> sub-TU balancer substitution is not always allowed in FRs, for example a splitter is a 2-2 FR regardless of its priorities, and it is also a TU balancer if it has no priorities, so removing its priorities would be such a substitution. But doing this substitution (removing priorities) in the 3-3 splitter square will limit its throughput. But it is okay in some cases, as my 4-4 and 6-6 LFRs using balancers show.
I've made some edits to my previous posts to reflect this information where relevant.