I've made the trip from Monterosso to the Berner Oberland a number of times. I find that the best solution is a departure at 07:33, arriving Interlaken Ost at 14:28 (time 6H:55M, 3 changes in Levanto, Milano Centrale and Spiez). As I mentioned above, the trip from Interlaken to Mürren will add about 53 minutes in travel time to that.
That's one of the quickest trips and will get you to destination in mid-afternoon which is a good time as your room should have been serviced. After check-in you can have a brief walkabout and then a nice meal.