Anything is possible with time an money but 9grand is a rip off!!!!
If you are sure that's it's not a load bearing wall they are easy to remove
You said you had a SE tell you it's not load bearing is there a wall directly above it?
If your dot an dabbing the whole wall it makes no difference what sound plaster that you leave on as the plasterboard adhesive will take up the difference when you push the board on to the wall
You can try cleaning it try soaking it in kettle descale but from experience it doesn't always work
You won't damage the pump by turning if off to shut the water turn the isolator valve check the water is off both hot an cold before taking shower apart
If valve is passed cleaning you are...
You can either dot and dab moisture resistant plasterboard or for tiling I'd recommend a cement based tile backer. Being cement based it doesn't rot unlike plasterboard as grout isn't waterproof
If you do use plasterboard buy plasterboard adhesive for dot and dab you don't need screws
You will find that it's not worth spending the money on repairing it as your due to have your bathroom replaced soon
Speaking from experience you will find the cost of spare parts on a lot of electric showers is expensive and sometimes cheaper to replace the shower unit
Your plasterboard will have been dot an dabbed on to the wall hence no visible screws, your best bet would be to drill through the plasterboard and fix a couple of screws into the brickwork