OK, I am waiting for the event processor to arrive.
In the meantime, I've learned this from TCE customer support:
The G-System has a MIDI mapping out. So for each user preset you can output a simple MIDI program change (without bank ref). In the MIDI menu, set MIDI PRG CHG to "ON MAP", then for each user preset, specify what program change you want to send out. You will be able to recall any of your Eventide user preset.
Silly me…I had MIDI-out set to "ON" instead of "ON MAP" and indeed, with the output mapping turned on it does send out only program change messages without the bank select. But also I noticed that with "ON MAP" there are no MIDI messages sent out from the factory presets at all….which shouldn't be a problem for me since I'm just using them as points of departure from which I build my own patches.
So, in summary:
MIDI-out "ON": bank select + program change sent on all presets
MIDI-out "ON MAP": program change (only) sent on user presets (only)
But I still need the event processor if I want to use the G-system to access any of the Eclipse patches on the memory card.