And the assumption that the OP made appears to be as a result of the e-mails not being clear on what the OT base was going to be. Bear in mind that the OP's experience was that the SD was included in the base for computing the OT hours when the OP worked over 40 hours a week. So it was not unreasonable for the OP to believe that is how it would work for the employer's offer. Thus, the fault for that lies with the employer, IMO, for not being clear enough as to how the pay would be computed.
The OP might not have worked any hours before the employer clarified how the pay works. My posts have been pretty clear, I think, that the OP isn't going to succeed in getting paid the higher amount for any work done AFTER the employer clarified how the pay was going to be computed.

