On the tap tempo:
I’m pretty sure you can do this. I’ll have to experiment to work out an appropriate work-flow (much of this will depend on if you’re wanting instant tempo changes in a live setting, or to fashion a tempo track while ‘recording’ a part), but I believe it involves first using the linear time mode while recording. Use a local MIDI transformer to convert your pedal stomps to a MIDI note on a track of its own (also set to linear time). If you like you could even assign that stomp track to some sort of Metronome click sound (You could use a sampler track, or send it to your favorite VSTi drum kit).
You’d want to use another local transformer to filter out your pedal events (or you could just run a quick logic editor to delete them later) for the track(s) that are recording your playing (minus the pedal stomps).
So effectively, you’d be recording 2 tracks at the same time. One holding your live playing, and the other holding your pedal stomps. Later, you could ‘merge tempo from tapping’’ and Cubase would create a tempo track for you. Go back to tempo mode, and hopefully things line up with the tempo grid all ready for possible quantification if desired.
On changing tempo via Continuous Controller:
It think this is possible using a Generic Remote map and a Virtual MIDI port. You’d need to record your live automation on a standard MIDI track which would be diverted into a Generic Remote Map via virtual MIDI port (Use something like loopMIDI if on a Windows PC).
I haven’t tried it yet, but It also might be possible to use the Generic Remote maps to bind a pedal based CC to ‘tap in a tempo’ during live playing. The catch here is that it’d only work in ‘fixed tempo’ mode. On the plus side, you could again use a virtual MIDI port and route the pedal(s) through a MIDI track and into the Generic Remote map; thus, making it possible automate the process of changing tempos on fly in a hand’s free manner.
Generic Remote maps offer a lot of not so obvious power user abilities. I’ve discovered a lot of interesting ways to automate DAW features that don’t have dedicated automation lanes using a regular MIDI track, virtual MIDI ports, and multiple stacked Generic Remote maps. Examples include automating things like arming and disarming tracks, launching macros, logic editors, and more.