For stuff like turning on the TV I use an alexa defined ( in the Alexa app ) routine that triggers an openhab rule. This works I would say fast. You can define routines in the Alexa app while LastVoiceCommand was/is nice to trigger the same rules/commands together with room awareness while I think you would require several Alexa defined routines to achieve the same ( if possible ).
You also could write you own “skill” defining your own intends and actions to be executed.
I have a self hosted ( on Pi ) skill written in python. Something like “alexa start jarvis and switch to channel 2”. “alexa start jarvis and ask what is currently running on TV”. In the background then http is being used to either switch the channel or check the what currently is active on the receiver ( either a recorded show that is being running or the current show that is received in live stream ).
