Semi-NCA hadn't even been published yet and seems like the clear choice nowadays, so I'm glad to see it in place! Great work!
Semi-NCA was actually published back then, just not in the cited paper.
See "Finding dominators in practice", published in 2004, section 2.3. So two decades ago.
The main advantage of Semi-NCA (and why LLVM uses it) is that it makes for a good incremental update algorithm. See https://reviews.llvm.org/D34258
Truthfully, as much as I love Cooper and friends (they were responsible for a lot of very thoughtful, well engineered algorithms at a time when lots of stuff was just "here's some research i think is better"), the "simple" dataflow based algorithm was never worth it.
Part of the thing i was good at way back then was keeping track of all of the research in compiler opts and which was any good - most of their stuff is very good.
I used to go through every paper that came around and keep an up to date library of ones worth looking at (both now and in the future) that a bunch of folks used. This was harder back in the days of nobody really publishing code, i used to have to write a ton of prototype implementations to see which numbers were real and which were BS because they compared against crappy implementations or whatever.
SEMI-NCA was an obvious win - it was simple enough to implement and test, equally as fast as what existed now, and could easily be extended to incremental updates.
If you want to see what it takes to do incremental updates with LT, take a look at GCC's dominator update code back around that time period (I think it's unchanged since then, actually, but i haven't looked in a few years). There were a fairly small number of people who could understand the data structures and algorithms involved.