Of course you can switch a FET gate when it's positioned
negative, you just have to make the right circuit.
100uS is not fast at all.
You could make a (-30V + 5V) reference / power rail with
a 7805 regulator whose "GND" is -30V and "VIN" is your
local ground.
In that negative-referred 5V domain you could operate a
chubby 5V buffer as a gate driver (I have used parallel
74HC14 Schmitt inverters to drive logic level MOSFETs
at much faster than this). But I might suggest a GaN
FET (EPC, GaN Systems) as alternatives, they will be
much more "square" (do you care, or know whether to
care, about waveshape?).
Then the trick is to pass current down from a "+5 logic"
domain (0-5) to the negative domain (-30 - -25). One
scheme I use a lot is, use a PNP (or PMOS) cascode
(B or G = GND) and an inverter w/ series resistor driving
its emitter (source). Cascode will throw (VOH-Vbe)/Rseries
down to "something" at the negative domain. A same value
resistor would give you an adequate VOH, when driven by
that current, to drive a Schmitt gate. One drives 5 in the
hex logic gate chip, 5 drive FET. Simple enough.