I don't think your read is correct.
I also think the fact that we can't agree on how to read this language suggests that this needs clarification.
A SxS can certainly be "cycled" and "cocked." Neither of those concepts are unique to pump or lever action guns. Even a bolt action gun can be cycled and cocked.
A definition that is limited to what "cycled" means for a pump or lever action gun doesn't tell you anything about what "cycled" means for a SxS nor does it exclude a SxS from the concept of what it means to be "cycled." In this case, it's likely the authors never considered it, but even that would not have any bearing as language often has to address facts not considered and the intent of the authors has nothing to do with what words mean even if some would find it persuasive.
I think looking for ways to penalize someone for something that isn't clearly a penalty is an automatic no-no. If there's no clear rule that makes a certain infraction a penalty, then it should be no-call, just like "I thought I saw a miss" is a hit.
That said, I have never used a SxS in WBAS and I don't intend to start, absent my M12 going down mid-match.