Update: After goofing around with different things in sim mode, I discovered that the sim works just fine and all numbers line up the way they're supposed to when ADS-B is NOT in the picture. On the HITS side of screen, the altitudes are reported as GPS, all the HITS boxes are at their proper altitudes, and the ribbon says GPS ALT. However, when I turn on the stratux and the iFly gives that tone saying, "Hey, I'm connected now!" that that is when the 1) HITS boxes start lowering, 2) the altitude ribbon on the HITS side drops to 660+ (my actual altitude at home) and the ribbon says "IND ALT," and 3) the altitude on the chart side jumps to 10,000+ feet and varies at will.
Maybe that helps pinpoint the source of the problem My guess is the mismatch between ADS-B altitude and the sim's pretend altitude.
Still have to constantly fiddle with pointing the sim plane left and right to keep the XTE down.
Note: ADS-B mode indicates "out of range" during all this, as I started the sim at the airplane pickup point which is on the opposite corner of the US from where I really am. Jut in case that factors in.