Please help with bearer requirements for room-within-room sound room

Hi there, please if you can help with this I would be most grateful.
I am building a room within a room as a sound room on the ground floor of my house - so there is going to be a timber frame on a concrete slab...and bearers on the top of that frame to support my ceiling.

Unfortunately I do not have much height to play with...and cannot use the 45x120s mgp10 for the bearers that I had planned if I want a 2.4m ceiling height....

The distance - slab to bottom of joists (of the floor above) is just 2570mm
Floor - 10mm (thin laminate on polystyrene)
Ceiling - 3 layers 16mm firecheck gyprock - 48mm...call it 50!
bearers 120mm
Leaves 2390...just under the 2.4m....

I could move to 13mm soundchek gyprock - but it's still border line....and the recommmendation from the sound folk is to go with the 16mm firecheck.
I could also 'interleave' the bearers of this room-within-a-room with the joists above - but I am unwilling to remove the blocks between those joists as they are long runs!

My bearers are going to be spanning about 1920mm

Can I use 45x90s instead of the 45x120s - and if yes - what spacing do I need? I really don't mind lots of bearers as it gives me more places to screw the firecheck to!

Or is there an alternate material I can use as the bearer that I can screw my gyprock to?

Many thanks...PS I would MUCH rather over engineer than under, just in case I end up doing a 4th layer of gyprock.

Also the firecheck is about 13kg/m2 (36kg for a 1200x2400 sheet)

Thank you so much for your help.

P