After a few trial-and-error flights, I have found that doing climb and descent using vertical speed mode/LVL CHG (for the climb) works pretty well. I also found that the issue before was most likely a sim issue with wrong frequencies than it was the aircraft, as I was able to perform an ILS landing into KOKC as I expected it to work. There are still some weird small bugs, especially related to the LNAV and its pathing just after takeoff on some departures with rapid turning waypoints, but otherwise I have figured out how to operate the aircraft in a realistic manner.