I would recommend that you take a look at Advanced Button Controller by @stephack. It is a very nice package where you configure "scenes" whose properties are retained within the app and only a scene activation device is created.
I don't use Home Assistant but I would expect that you could have an iFrame in a dashboard in which case this might be of use to you in your final solution.
So:
- Configure a single virtual button device with say, 20 buttons.
- Define in ABC what each button will do. Each button has 3 actions so you would have 20 x 3 unique scenarios.
- Define in Remote Builder what commands to execute on various button presses.
- Embed Remote Builder iFrame in Home Assistant Dashboard.