The existing joists are 4" by 2" and are at present supported by
sleeper walls at 5 foot centres, the spacing between joists is 10"
with no noggins.

I built a deck for 2000kg hot tub last year. 6 x 2 joists at 12" centres
supported every 4'. Not a millimetre of movement!

Remember the depth cubed factor though - 6" is more than 3 times
stiffer than 4"