Seems you may have homed in on the possible cause. Must admit I have not, to memory, modified a saddle to perfect, or vice versa, from the drop-down in the Assembly Sections window. Have always used that in the process of creating a Stripping Sheet Template, as an 'up-front' step. Maybe that's a big ask of XMF to try and alter binding style on an existing Template. There may be specific parameters in place for that style that sends things off the rails when you change styles further down-track.
Having said that, I can't say whether it's written in the documentation as to whether you can or not.
I sure won't be trying it now though! Forewarned...
Addit: My compadre was having trouble sometimes, where he thought he was bringing in SSTempl sheets, but they would split in Assembly Sections, thus giving him non-saddle page-flow. The only thing I could suggest was that he recreate any SSTs that were giving him grief, from scratch. He's not big on feedback, but I haven't heard any cussin' since. Could be similar issue.