ony Williams writes
And (wait for it) the little mains filter that powers the modem
actually has a VDR across Line-Earth.

Noname (yet). All I know atm is that the nuisance tripping
*appeared* to reduce when that VDR was removed. The VDR
is marked "GE U9 275L40B", which probably means a 275V(rms?)
stand-off voltage.
Yes.
So that should be an ok design
No, definitely not. Should only be between L & N.
as long
as the VDR is not faulty, and on normal mains voltages.
Normal mains voltage includes very short spikes up to several kV, and
longer ones of several 100 Volts.
During these spikes the VDR is only 100 Ohms or less, so it can put a
lot of unbalance current thro the RCD for the duration of the spike if
your earth is fairly good.
These spikes can trip RCD's anyway on occasion, due to the house-wiring
capacitance to earth and filters on electronic gear, without the help of
spurious VDRs.
If your electrician gives your installation a clean bill of health, but
trips still occur, he can ask the supplier to but a transient recorder
on site for a couple of weeks to see if your trips coincide with
incoming rubbish. Normally foc.

You really didn't want to know all that did you, but maybe it will be
useful to someone else following the thread.
--
roger

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