I agree you need to work to 25mm per M, or 1 inch per M is how I was taught it.
(my old neighbour and plumber told me that regs say 18mm per m, all plumbers work to 25mm in practice)
I have used bath traps in the past where drop was an issue as they are deliberately designed to be very shallow. I guess it will come down to how standard the new shower tray waste hole is and what you else you can get to fit that, as if you are restricted to using that waste with 9cm drop I dont think you have a choice but to raise the shower tray – or redesign your bathroom layout (which may not be possible/practical) to be able to get sufficient fall to avoid issues with the pipe clogging.
I would look around – ask plumber to see if there is a different waste that fits the tray with a very shallow design.
Rereading your post you need min 80mm drop in the waste (pipe centre to pipe centre) so you need either a waste which is no more than 6cm below base of tray at the bottom of the outlet which seems very shallow based on a 40mm pipe, or raise the shower tray / whole floor sufficiently to get the waste to that height.