Full disclosure: I'm not a Harmony, Marantz, or Humax guy.

For many units the 5 second delay is too short. You need to experiment with the delays. If you are using the native receiver remote, how long must you wait after Power ON before you can reliably select an input? Use this as your delay. Same for the TV and Humax.

Also, you may be having a CEC (Consumer Electronic Control) spat. The idea here is that you can give a command to a "box", such as a DVD player and it will communicate with other devices using the CEC pin in the HDMI connection. The plan is that with a single DVD Play command, all of the other boxes will power up and select the correct input. Unfortunately, this does not always work as intended. Installer Pro's hate CEC.

I can't give a full CEC tutorial here and you'll notice that a manufacturer, such as LG, will have a private name for "CEC". You can search for CEC information. Be prepared for many complaints and "sure fire" solutions that don't work. Sometimes the best approach, especially since you have a Harmony, is to simply turn OFF CEC for all of your boxes and manage power and input selection with the Harmony. Unfortunately, some boxes require CEC to be enabled before some basic features, such as surround sound or video modes, can be used.

With respect to disabling CEC you can also insert a CEC blocker in the HDMI cables. With the blocker installed, you can enable CEC on a box, but it will never actually send or receive any CEC commands. I've had to resort to using these a few times to suppress rogue commands.

Is HEOS set to autoplay? Another wild possibility might be that a defective remote will ghost press a button. You could test this by keeping the remotes in a closed shoe box. This will block all IR commands. If this stops the HEOS issue, then bring the remotes out of the box, one by one, until you find the "ghost".