Question about deflection in joists

How’s it going guys? Currently doing some works where we’ve got an old set of floor joists which have a bit of deflection when walked on from above.

We want to sister up the joists with fresh timber to a) add strength and b) level out the surface to add drywall and wet plaster over the top. Building control is 100% happy with the joists as is but longevity of the plaster and drywall will be effected if screws start popping as the wood flexes.

The problem is, if we level the stud work out we’ll only end up with 50% of the new timber in direct contact with the old stuff on one end. In my mind, this won’t affect the strength of the new material as the deflection still has to bend the entire width of it.

Does this sound about right?