Insulation, Radiant and Vapor Barriers - Liveable attic insulation

greetings, I'm wondering, I bought a 50 year old house, it has a liveable or convertic attic. they had particle board over sheet rock everywhere upstairs, i am currently moving this and will be re- sheetrocking. The ceiling insulation was obviously incorrect as the insulation was pressing firmly against the roof and is useless, it literally burned on the paper that was pressing against the roof. I have 2X6 joists, what R value insulation should I replace this with? I live in Long Island NY - climates from 10 - 90 degrees. It was suggested to attach a 2x3 to each joist and install R19, is it neccesary to extend each joist?
I do have soffits and am getting a new roof with a ridge vent. Thank you for your insight!
Regards,
Sean

The ceiling insulation was obviously incorrect as the insulation was pressing firmly against the roof and is useless, it literally burned on the paper that was pressing against the roof.

For sure paper side to the room.

Id say all you can put into what you have now is R 13. so you have air room above it to the roof

It was suggested to attach a 2x4 to each joist and install R19, is it neccesary to extend each joist?

YES

I think it would pay you back for sure to go with the R-19 there. dont forget to put the foam rafter vent up first so air can get over the top of the insulation in all the rafters. Id check it out .But you might get by with just add a 2X2 in each rafter for the room for the R 19.
You do have vents in the soffits RIGHT
ED ;)