Voteview has a very interesting look into my last post. I highly recommend it for those interested in the problem. They run an experiment by eliminating all the close roll call votes in Congress and measure polarization. After eliminating these votes - 94% of the votes they analyzed passed by higher than 61%, which should eliminate most party votes - they analyzed the data. We can only glean so much from this data because it is not a direct test of procedural v. substantive argument. However, there are a couple points to be drawn out from the analysis. First, the polarization trend is the same. In other words, if we assumedly eliminate most of the procedural roll call votes we still find polarization with the same trend, though it is much less intense. In short, polarization exists after the supposed elimination of many procedural votes from the analysis. This is important to note because members are polarizing on substantive issues. I mention this in the conclusion of the first post: procedural votes have exacerbated polarization, but that polarization between the parties on final substantive votes still exists.
Second, another interesting test, though limited, would be to examine the close votes (those under 60% passage) separately. Given the difference between the original polarization line and the lopsided - aka close vote omitted - line, we would expect polarization on close votes to be higher. This is not at all surprising but it does highlight a point. At a bare minimum, it corroborates Theriault's overall argument in his 2008 book, Party Polarization in Congress. Again, this is not a direct test of his argument. But at a bare minimum, as much as the analysis supports the contention that polarization exists even without close votes, it also supports that close votes (of which a large chunk are assumedly procedural) also intensify polarization.
It is important to remember that Theriault is not making the argument that procedural votes are the sole cause of polarization. For the sake of brevity, I omitted many nuances of his argument, which is really an injustice to the very extensive work he put into his book. Constituency change, gerrymandering, party organization, etc, do play an important role. That said, Theriault does argue that most polarization recorded in roll call votes is the result of rules changes. Regardless, the voteview post is very interesting look into these trends for anybody concerned about polarization in Congress.