How to deal with routing density issues near uController
You have a few options.

You neglected to mention which PCB house you are using.  Change to a PCB house with tighter tolerances, copper filled microvias, and smaller pad to drill size. 

You neglected to mention which router you are using. A better router may help. 

Look at the density of the routing, most CAD has a density map.  Open up the power plane where the density is high.  

You could also switch to a hash pattern with the power and ground leaving some area between the traces for signal routing. This could also be done just in the high density areas.