I am afraid you won't have a chance until Aodyo gives us controlling possibilities like setting the base note by sending something to the Link and sync it to the instrument or vice versa or what-do-I-know ...
Just loud thinking:
Do not change the base note on the Sylphyo but rather at the destination. Near the MIDI input, in Cantabile, before the plugin, whatever is possible. It's only about adding a value to incoming note numbers.
I don't know how you operate the EC4, but if pushing knobs doesn't interfer with other functions I would use the push functions of encoders 1-11. They have labels and pressing the corresponding knobs makes manual changes more or less failsave.
If you can send SysEx from Cantabile or through another software, maybe Aodyo can give you a string to set the base note on the current Link. You wouldn't see the change on the Sylphyo but I think you could live with that.
If you can program that in Cantabile or in another software, you could switch the base note on the Sylphyo, then do something on or with the Sylphyo you never do while playing (telling the software that the base note is coming) and then play the base note. Like a keyboard player handles key switches.
None of the above is an ideal solution, but maybe I could give you some ideas.
Just a note:
If you need MIDI processing but don't have a software for that, consider Bome MIDI Translator Pro. They have a very helpful support guy in the user forum. BomeBox could be an additional option but that little monster is expensive.