Here are some ideas that might trigger your brain to help track down the basic problem:
Firstly, what is the spec (and preferably the exact model) of the existing RCD (so that the trip characteristics can be identified)?
Secondly (& possibly regardless of the first question) do any of the newly fitted units have switched mode PSUs?
Asking that because (as you already know) the input rectifiers on those have large high voltage reservoir caps - and if those have discharged over time because the device has not been recently used/triggered then the PSU inrush current can be very high indeed. If the latter is not very well controlled (i.e. lack of NTC thermistor etc) then some types of RCD also have over-current protection facilities could trip ?
OTOH, one or more of the new devices might have input over-voltage protection in the form of Gas Discharge Tubes (GDT) or Metal Oxide Varistors (MOV) which are tripping due to incoming line voltage spikes - causing a momentory major Line/Neutral current imbalance and thus tripping the RCD?? NB: GDT's etc., can also result in high "standing" earth/ground leakage currents, which might then only require another brief source of extra leakage current to drive an RCD to the trip level.
What could cause that sort of spike? Local lightning strikes (might not even hit the supply cables!) could induce them, or maybe a large motor (e.g. for a lift, or the entry gates) that is only started very occasionally, because it has been known for that sort of equipment to cause quite major radiated &/or conducted EMI if situated very close to sensitive equipment in office blocks etc.
As for fitting that additional RCD & socket, see the First Question to start with!