Strengthen floor joists from below

Hi,

Room above is a bathroom and has already been renovated so access from above is not possible however an old leak where the cylinder used to be means a good portion of ceiling below needs repairing and I was going to take this as an opportunity to put some sound insulation in the floor so rip it down and throw up some new plasterboard.

The joists are quite small (5.5 inch x 2.5inch) with tiles above so I would also to take this opportunity to strengthen the floor as I think we're borderline on the deflection front and I dont fancy doing the floor again.

All the electrics unfortunately run opposite to the joists so sistering is not an option, however there are 2x2's which have been fixed to the bottom of the joists (running with them) to level out the ceiling in the kitchen/extension.
Could I just turning these 2x2s 90 degrees to create a lattice system below before fixing new plasterboard? They are needed anyways to keep the ceiling flush but currently offer no load distrubution benefits.

How much cabling are we talking about? It wouldn't be the end of the world to cut a few wires, sister the joists and then rewire, running the cables through matching holes in the sistered joists.

Alternatively, putting noggins between the joists would also help stiffen things up.

@Lower too much im afraid...plus all the pipes (bit of a mess really not where I would have run services) so it really is a no go in my opinion. Extra noggins will provide some additional support (especially around board joins). Would just changing the direction of the 2x2 also be useful to help spread the load?

I don't know why they didnt replace the joists with deeper ones when it was originally done instead of fixing battens to the underside

It might help a bit, but full height (or as close as you can get to full height) noggins would be much better.

In that case then I could get some 7x2 noggins in there. Building extension at the moment so I've got alot of 400mm offcuts!

I'm idly wondering about whether it would help to fix metal strips along the existing joists, running above and below the wiring?