I agree with your answer, but not your argument. Look closely at mechanism A - this mechanism involves an SN2 substitution reaction, using I- as the nucleophile and the carboxylate anion as the leaving group. If it was merely a question of stabilizing a positive charge, the primary carbon of the methyl ester would be less stable than the secondary carbon of an ethyl ester. Stabilizing a positive charge would argue an SN1 mechanism, and ethyl cations being more stable than methyl cations, you would expect the ethyl group to react faster, not 10x slower. However, sterically, an SN2 reaction is much faster at a primary center than at a secondary center. The presence of an extra methyl group partially blocks the backside attack required by an SN2 reaction , and I- is a very large atom to try to push in.
The reaction at the carbonyl center in mechanism B is an addition reaction, and sterically would really only be affected by atoms directly attached to the carbonyl carbon, unless there was some sort of ring system to pull groups around. The atoms attached to the carbonyl are identical for both the ethyl and the methyl ester (they both have a secondary carbon on one side and an oxygen on the other) so you would expect very little difference in reaction rate from changing a methyl ester to an ethyl ester - the change is too far away from the reactive center.