Diet could be playing a part in the shell issue, especially since you said you were feeding spinach in the past. This is why some alternative foods were mentioned that would help your turtle shed scutes.
Shell problems can be the result of a number of factors, both dietary and environmental. The white is under the scutes and the scutes are hard? To me, the white areas in that pic you posted look like those areas on the scutes could be trying to flake off, not shed in one piece.
Basking under correct lighting is important as well, since it allows your turtle to metabolize UVB rays into Vit D, which is necessary for calcium absorption (and a healthy shell).
If your turtle had mineral deposits on the shell, they'd be on the scutes, not only under them.
A lack of Vit A doesn't cause pyramiding (overfeeding and a high protein diet causing fast growth are usually the culprits), so I'm not sure what you're talking about there (I also don't remember seeing pyramiding of your RES's shell). A lack of Vit E will contribute to retained scutes and difficulty shedding them.
What pellets did the vet recommend?
What kind of vitamins are you supposed to give? If your RES is deficient in Vit A and this is the vitamin you're supposed to give, it would be better to feed foods high in beta carotene (pumpkin, sweet potato, carrots, etc.), which can be converted to Vit A without any concern of getting too much (Vit A can be harmful if overdone as a supplement).
