Good news (phew)!
There are indeed direct input commands in the library for the Samsung, so I was able to program the Harmony 300 "Watch TV" button to power up the TV and the Humax, and then force the TV to HDMI2 (I switched the inputs while playing). It also powers down both if pressed again.
I was not using that button because I was worried what would happen if one device picked up the command but not the other, but this is the lesser of the two evils. It is most likely to be a problem when the batteries are fading. Now all I need to do is write detailed instructions what to do when the Watch TV button doesn't achieve the desired effect.
There were no HDMI sync problems while I was playing, that might have been a red herring.