So I called tech support, and was on the line for hours trying to recify the situation. Republishing, creating a new database, reimporting the tables, messing with settings, and many hours later, we were no closer to a resolution. Telerik Fiddler showed "500 internal error" with no description of the issue, and the logs were no help at all.
After no resolution from tech support, I tried the tactical nuclear option of recreating all my tables in arc. I had suspected this was what I had to do, but was avoiding it for the sake of maintaining database integrity. But creating a new table, and making sure the field types were correct has seemingly fixed my issue. I suspect that it was a data type issue, as we had imported all of the files from an Oracle database to an SQL database. There were many known issues of Date/DateTime fields creating problems, so I suspect that may have been the hurdle.