Replacing first level joists in tight area

[Paulie80]

Hi, an 80s dormer conversion was added to my bungalow and i'm in the process of making a section of it into a bathroom. The floor had some bounce and squeaking and I planned to sort this. The issue was clear with 6x2 joists being nailed into the 95mmx38mm ceiling joists. The nails werent fully secured and all could be rocked from side to side. 4 of the 6x2 joists had be cut which added to the bouncy'ness. The ceiling joists are solid. 

 

I've taken the cut 6x2 out and plan to replace with 7x2 I have left over from another project. The issue I have is I cant disturb the ceiling below and the gas/water pipes on the right mean I cant get a full length into the wall holes on the left.

My plan is the use a ledger board/wall plate on the left for the 4 new joists. Slide the joists in first on there side to fit under the pipes and then fit the ledger board which the joists will hang from. Have the nodding also attach to the ceiling joist to lock everything together. On the existing 6x2, use m12 bolts with square washers to secure properly. On the right is a wall which the joists will sit on. Below is my plan.

I appreciate this isnt ideal, wondering if anyone has other suggestions? Thank in advance.