No, it shouldn't be that the filter is too big for the pump. Something else is going on. Usually new sand doesn't filter quite as well as old sand so that's probably not the problem. And the dead algae SHOULD be gone.

When you back wash, is the back wash water cloudy in the site glass? Or clear?

Why not put the pump on a timer and run it for 2 hours 2 or 3 times a day and see if that does away with the problem? It would be a work-around.

I must admit I'm thinking something ELSE is going on, either in the multi-valve or in the filter's laterals.