To answer the original question:
If you look at the equation for R/C, you see that among other things, weight and excess thrust (and in turn total drag, because excess thrust is approximately equal to total thrust minus total drag) play a part. Given that we're talking about a 777 at MTOW, weight obviously remains a constant (if you want to disregard the use of fuel and resulting slight decrease in weight during climb). Thus, the main variable is total drag (or excess thrust). Less drag, better R/C.
Now, the drag depends on many lift-related and atmospheric variables, which can easily change. Drag is also indirectly affected by the various speed restrictions, etc., that you mentioned. Because of the many changing conditions, you can't really calculate R/C with the information you've set out as givens -- total drag depends on a lot! Even the optimum cruise altitude you talked about depends on a multitude of changing figures!
Again, R/C really depends on a lot!!!
Also, all that is the purely aerodynamic stuff. "Real-life" conditions come into play, such as a more economic climb, airline policies, etc.
Alright, I've rambled on enough. Sorry,