I have a basic concern about this assembly, which
I take to be an inrush current limiter (by way of rail
dV/dt ramp rate).
Your turnon plot appears to take 2 seconds to
slew. That's a long time to be holding a power
MOSFET linear. I would worry about the load
/ filter bank being able to cook the channel
or neck. I think at the least, you want to qualify
the MOSFETs you picked for the Joule energy
they take, and try to figure (or better, measure)
local temp rise and deduce reliability.
Or maybe you do something like a compound
output, use big dumb power BJTs to handle the
linear interval (they are made for it, no fancy
assumptions that they are "either on or off"
embedded in the conditions) and hard-switch
the MOSFETs once the two BJTs top and bottom
have buried into saturation. Everybody working
how they like to work.