To be honest, I don't really see your problem.
If you really have 7kV common-mode on the lines, then your design is probably very bad.
I'd say everything above 10-100V of CM voltage would be a real problem.
The coupling-clamp for the burst test has a defined coupling capacitance (I can't remember the value from my head) which forms a voltage devider with your filter (and parasitic) capacitances (and CM-chokes if present) to ground in your EUT.
In addition to this, your generator should have a source impendace of 50ohm IIRC.
So you will never have the full 7kV on the lines.
Whenever I have such problems to trace down, I usually put the probes at the input pins of the IC inside the EUT.
So I use the filtering/protection circuity inside the EUT to protect my scope-probes.
At this location you should stay well within +-20V (CM disturbance+signal) for common communication applications...
The worst case would be to use an isolation transformer to get the impact of the coupling to ground from the scope further down.
Usually you need to do this if you find your device working whenever you connect the scope
![Smiley :)](https://www.eevblog.com/forum/Smileys/default/xsmiley.gif.pagespeed.ic.R8GFI-pF6f.png)
BTW there's the cleverscope:
https://cleverscope.com/products/CS448To be honst, I just got a marketing presentation on the features.
I have absolutely no experience with the real product but the numbers sound quite interesting:
Isolation Capacitance< 14pf Channel ground to chassis
Isolation Capacitance < 6pf Channel to channel
But your idea has another very interesting aspect.
Whenever you get the opportunity to trace down problems in some high-side-gate-driving circuit, that isolated scope would become quite handy.
There you really have signals "jumping" some 500V-1kV wrt ground...
73