I'm think I'm going to go with what you said toward the end: "The different interpretations about how to go about grading without grading your own students' papers is very frustrating." In my previous email I was too sure of my own interpretation.
There seem to be different rules for SLOs and for Regents, different rules in different districts, and unclear interpretations of the various rules. We went with the idea that if a Geometry teacher helps us (indirectly) grade an aspect of a question, then she's influencing the scoring of her own students. But if that's not allowed, then the idea of Geo-teachers-can-particpate-in-the-grading-as-long-as-they-avoid-their-own-students'-papers should not be allowed, and that is allowed, at least according to our region. So what the heck? And when we ask questions about what's allowed, I don't have much confidence that those giving the answers really know, since the state hasn't been at all clear.
In the end our department decided that even though we were told we could have teachers of course X participate in grading for course X (as long as they avoid their own papers), it would be simpler and more clear cut if we they just didn't grade their own course at all. And as we've been grading we've been very happy with that approach -- less tension and less emotional involvement if just those of us not teaching course X do the grading. (That's not a criticism of those with emotional involvement.) And our department works well together and is very careful and professional in our grading. It's been working out very well.