Your left rear spacer is also an Izzy 308 component. I can't tell you for certain that this will impact feeding in 30-06, but it certainly is not necessary. It might be part of the problem, I just never tried shooting 30-06 with it in place. Just try one thing at a time, so you are certain what impact each change makes. Definitely, as GUNNER 50 points out, you want that cylindrical right front stop installed. Or, you could get one of the screw-in versions of the USGI short round stop, rather than having to rivet the stop in.
Next thing, is your 30-06 ammo to mil spec overall length? The Browning requires that, unless you use the USGI short round stop that I mentioned. Short ammo will tend to slide just far enough forward that the extractor can miss the rim, and there's your failure to extract from the belt. But the missing right front stop might also let the ammo cant a bit, nose to the right, which could potentially interfere with the extractor function as well. So let's start by confirming the ammo is mil spec, and go from there.