I have a 12 year old brick chimney pulling away from the house - 1 to 1.5 inches at the top, nothing shifting at the bottom, in fact the bottom 20 feet of the chimney looks almost brand new, not settling cracks,etc.
Above the roofline the bricks are spotted with white, probably the original installer used a different mix for the top of the chimney. -
I just had 3 contractors come out with 3 proposals
Contractor #1- knock everything down and rebuild - using old bricks where you can - using the anchor system all the way up. - cost $6500, with all new brick $7800
Contractor #2 - knock down only from top to foot below roofline - rebuild with new bricks, use one or 2 course with anchor system - cost $6275. (seems too high)
Contractor #3 - don't know down anything, go into attic and drill masonary anchors through the rake board and a metal support right into the bricks - also grind out pointing from roofline to top, recrown and repoint - recaulk entire chimney cost is $1500.

Any thoughts on these proposals - what is the opinion on #3?

I'd go with option three. But I'd have him put an piece of angle iron across the far side of chimney and run threaded rod through ceiling joist.

I am assuming that chimney has pulled away from house because of tilting. That tilting is probably caused by settling.
After 12 years, chimney has probably settled all its going to but you don't know.

Tying rake board to chimney will not prevent further tilting. Tying chimney to ceiling joist might. I don't think roof rafters will provide enough resistance to further tilting.

Run rod through several joist, then brace between joist with X so you get the resistance of several joist.

This what I did for a customer. Whether of not it will prevent further tilting, I don't know. Have to go back in 5-10 years to see. It did close up the gap between the chimney and house siding enough to allow me to seal the opening with 1/4 round molding.