Running the 'scope off a battery (or just a plain
old isolation transformer) would free you from
common-mode limits but the differential voltage
comes down to the vertical channels' front end.
For a power inverter you might assume you do
not care about milliamps, so maybe just make
a resistor divider per channel all returned to the
same ground, maybe 990/10 ohms and now
you have a 1/100 scaled voltage that ought to
play with regular probes just fine, and with a
7pF tip the time constant is still sub-100ps, way
faster than any inverter's edge rates and pulse
widths. Might need to take some care with the
power ratings and tempcos, creepage and so on.
Maybe make the "990" out of (10) 100-ohm
segments and one of those, a parallel 1K. Or just
take the real scale factors and forget round
numbers, which would take up the tolerances
too.