Someone else will have to answer about how good the tape delay is (although given that it’s Empress, the algorithms are likely to be excellent) and your questions about what it features.
You could change parameters to set values (or a rise/fall at any speed you want) via the 3 stompswitches, or set min/max and ramp speed to an expression pedal, or external MIDI, or place a button on the grid linked to what you want to change, or use a sequencer controlled by any number of different methods… there are loads of possibilities and I’m sure I haven’t listed many of them! But yes, the Octatrack could do it.
Or use the big controller knob if you’re happy changing things one parameter at a time.
Ping pong delay has its own separate module. You could even switch between ping pong and stereo on the fly using the aforementioned options if you set up 2 delay modules (one stereo, one ping pong) and established some kind of control link between them.