1) Did you try all the "Inputxxx" commands in Device mode? By default, the Harmony Adjust Inputs is configured to use Method 2 (discrete method). Most AVRs support discrete input commands even if they are not on the original remote. If the discrete commands work properly in device mode, and the Adjust Inputs configuration uses the correct commands, then try increasing both the Inter-Device and Inter-Key delays. Make them both the same value in case the "criss-crossed" and/or "added together" bug is still present.

2) Did you change the address mode of your AVR? Many AVRs support alternate IR addresses. If you did, then the Harmony dataset will not match. You got 2 choices. Set the AVR address back to default, or, on the Harmony user interface, do a Device > Settings > Confirm infrared commands. It will ask you to send a few commands from the original remote to find the alternate IR dataset, or ask you the teach it the alternate set of commands. However, if you need to teach it the alternate dataset, you may not be able to teach it the discrete input commands if you don't have them on the original remote. In this case, you would be better off using the default address that has all the discrete inputs matching the Harmony database.