Sagging 2nd story ceiling

[Trapper]

I have a room that is 14'x12' and the center is sagging about 1 3/4"
The house was built early 1900s and the roof is a rafter style built with true 2x4s and the ceiling is the same.
I have stripped all the plaster but left the lath because it has 12"-14" of blown in insulation.
My plan was to cross run 2x4"s on the ceiling every 24" and notch and cross run the opposite way every 4', brace the ceiling up and then put in nailers to the rafter from the ceiling to hold up the sag. I would also be gluing and screwing everything in place, then gluing in 1 1/2" HD foam in between the 2x4s.
My question is would truss plates work or would it be a better idea to angle the board to nail or screw into the sides of the rafter and ceiling.
I am open to suggestions.
Thanks for any advice.

 

[havasu]

I believe you be better off sistering each rafter with a 2x6. That span is too great for a 2x4 alone with 24" on center.

 

[Trapper]

I believe you be better off sistering each rafter with a 2x6. That span is too great for a 2x4 alone with 24" on center.

Thought of that but didn't want to tear everything out, my main goal is keeping all the insulation intact.
It has been up there for over a 100+ years doubt/hope it's not going to go anywhere.
I have all the slotted 2x4s running opposite across the originals and have the ceiling lifted and next will be securing to the rafters one way or another.