Ok, for the record, I did some extensive testing recently. I have both a Roland FC300 and a Novation Remote SL 37 which can send all sorts of midi messages, CCs, sysex, etc.

So to answer my question and to perhaps help other people in similar situation, here are my findings. I will also post some feature requests as suggested by Hugo above to improve the MIDI support on the Spider Valve. With a bit of luck maybe it'll work, who knows. Anyway, here goes:

- Wah on/off: can be controlled by a midi sysex (no CC): the following worked for me:

  ON:   F0 00 01 0C 12 06 63 00 00 09 00 00 01 F7

  OFF: F0 00 01 0C 12 06 63 00 00 09 00 00 00 F7

- Wah position: CC4 seems to be it, as suggested by the manual, but it does not practically work as the wah effect turns itself off as soon as the value is changed. But if I turn it back on (using the on/off switch above), I can hear that the wah position changed (as the wah tone changes, it either has more treble or less depending on what I did...). So it works but there's a bug I suspect. I don't know how the FBV manages to do it then, would be interesting to hear from Line6 (must be something else than a MIDI message).

- Volume pedal (CC7): The same thing happens with the CC who's supposed to control the volume pedal (as mentioned by the MIDI implementation manual). Whenever I change CC7's value, it seems like the volume changes for a second but instantly resets itself, as if something else was overriding it. So that also does not work, and seems to be having the same behavior than the CC4 somehow (another bug I suspect). I tried using this to control the pitch pedal position, because there's a setting somewhere to control the pitch with either the volume or wah pedal.

- Pitch glide (aka whammy): can be somewhat controlled via midi CC27, which is the "stomp FX swoosh position" as mentioned in the manual. But unfortunately that is not the same as controlling the pitch pedal position, but rather it is changing the "heel" setting of the pitch effect. So when you play with that CC, you hear something like a whammy, but the control is not as precise as with the actual position (pos) parameter of the pitch effect. In particular, the heel parameter only changes in "rough" increments of +3 / +5 semitones and avoids the 0 position (neutral or the same tone as the original) which prevents one from making something like a real whammy. Hence why I said you can emulate a whammy but only to a small extent, which is a big bummer.

- One funny thing I noticed, the pitch effect's position CAN be controlled with the midi Pitch Bend message. That's perhaps how the FBV does it, I dunno. But anyway, I don't know of a midi foot controller which sends pitch bend messages (found that by accident with my Remote SL midi keyboard) so this is useless to me, other than being anecdotal...

- Looper: there's apparently no midi messages to control this, sadly.

Hence it seems like these are all small issues / bugs (aside from the looper) which could easily be fixed and/or patched by Line6 to provide better midi control of the amp. I will also send this as a feature suggestion to Line6 support.