Roof Rafter/Beam Joint pulling apart and sagging

You have 2x6 joists 16" o.c. and lets assume #2 fir- the MAXIMUM spam (where they are supported underneath - bearing the weight) for a 20 lb dead load is 9'10" and for 10 lb dead load: 13' 2"
You show 11' +- in photo but it is unclear if there is support at that point. you can check span table at: https://www.awc.org/pdf/codes-standards/publications/wfcm/AWC-WFCM2018-ViewOnly-1711.pdf

There is some interesting framing in that attic: The 2x4 at the peak of the triangle which is set on top of the ceiling joists is very odd, in my opinion. It is transferring a load from the roof to the ceiling, and unless there is a wall underneath: you probobly have a bow in the ceiling at that point below.

Soooo: minimal storage, depending upon support at the 11' 3/4" point - Once you put a floor downs there even with the intentions of keeping it light up there - people forget in time.. . . .

As to the beefing up the joists with 2x8s that is an option - but the total span is more important. Is the entire width unsupported? and if so what is that total span?

Your plan is exactly right, except that you don't need such heavy-duty hardware to do the jacking/winching. Even a pair of motorcycle ratchet straps or a come-along is going to do the job, especially if you jack up the ridge board. I think it'll all move easier than you anticipate. Just make sure you have solid connections to the walls so you don't have any sudden surprises if something lets go. Maybe lag some loops to the top plates.

One or two rafter ties, well-attached, will prevent the problem from happening again. You could probably get away with keeping them a foot or so above the wall plates, too, if headroom is at a premium.

Good luck.