I do MORSE, an undergrad course, so can't answer many of the things you are asking about, but can offer a few things.
I would honestly say the Warwick course sounds the best, followed by LSE, followed by Edinburgh.
Though it is close between Warwick and LSE.
Warwick's performance in statistics, maths, economics and business is among the best in the country.
To be honest, you are unlikely to find anyone who's done MSOR itself on here.