Great. Now do 40 apps and try not to get them killed by the OOM mechanism. I'm not saying I like the fact that messages go through Google's servers, but I'm afraid there is no equivalent FOSS solution.
At least on Android you have two options: you use Google's notification API which lets your app sleep until the system wakes it back up on receiving a notification. Or you skip all that, then your app has to run in the background or you won't get notifications. You can guess what this does to your battery.
Do you actually need the GUI or is it simply a preference? Because investing 15 minutes in a proper ffmpeg script might be worth looking into.
Apart from that, what would that hybrid "ffmpeg-then-Handbrake" approach look like? What would be the goal here?