I’d go for that M665, and yes it will fit your M770 cranks. What makes it double specific is that most 36T Shimano rings are designed to work in a 26/36/48 combination, whereas this one is designed for a 22/36 combo. Specifically it has differently contoured ramps, tooth phase, and a ‘deeper’ ring – all designed to make the shifting between the 22 granny and 36 big ring as trouble free as possible. Its difficult to describe all these features, but if you put a ‘normal’ 36 ring and the M665 next to each other, the differences become obvious.
Now, I’ve had this debate here and on other forums before – and I know many have used other 36 rings without problems. Equally, a number of people have had chain rub & drop and clunky shifting by using other 36T rings. Personally I’m anal about my shifting, and expect it to be as smooth as silk, and I’ve tried other 36 rings in combination with a small granny, and the M665 is definitely the best.
Now the negatives. Its alloy, so will wear quicker than a steel Deore 36. Secondly, it’s real ugly – but if you’re hiding it with a bash this won’t be a problem!