Question about oxygen and beta carbons in chemical shifts
I think perhaps you are misunderstanding some basic principles of determining chemical shifts. I have no idea where you are getting your +0.5/+0.6 factors

Chemical shifts are a product of all contributing functional groups; those that contribute to the local electron density either through direct electronic effects or through steric effects. Looking at the 3 proton environments, we can roughly predict their chemical shift using additive tables (I use Pretsch, Buhlmann and Badertscher).

First, let's look at the types of protons. Methyl protons and methylene protons do not have the same basis chemical shift to work from when doing additive calculations; the shielding from a C-C bond is not the same as for a C-H bond, and so the local shielding for the proton of interest will be different. Generally, when doing additive calaculations for chemical shifts, we can use the starting shifts of 0.86 (-CH3), 1.37 (-CH2-) and 1.50 (>CH-).

For this molecule, there are 3 proton environments. I have shown their predicted chemical shifts below. 



For methyl protons at site 1


Each -CH3 proton is alpha to a quaternary C, beta to an oxygen-bound ester and beta to a carbon-bound ester. 
So that gives us 0.86+0.05+0.44+0.07= 1.42ppm


For methylene protons at site 2


alpha to a ether oxygen, alpha to a quaternary carbon, beta to an oxygen-bound ester and beta to 2 methyl groups. 
So that gives: 1.37+2.04+0+0.24-0.06-0.06= 3.53ppm


For methylene protons at site 3


alpha to ether oxygen and alpha to carbonyl-bound ester. The ester oxygen is taken into consideration as part of the ester group as a whole. Also, the atom on the other side of the ether (in this case the carbon) is taken into consideration - The only important thing here is whether the ester is oxygen-bound or carbonyl-bound. 
So, that gives us 1.37+2.04+0.92= 4.33ppm