Different contributor here. Please permit me to assist. First, to clarify, there is no, "your answer" with respect to Justanswer, because every attorney who answers questions in this forum is deemed an independent contractor, no one coordinates with anyone else, and as you are already aware, attorneys frequently differ in their opinions about the law (which is why there are judges, because someone has to figure out what the law actually is ;->).
The general rule of the Contract Work Hours and Safety Standards Act (CWHSSA) (40 USC §3701 et seq.; 29 CFR Part 5), is that prevailing wage payments are required for work "covered by the contract." Clearly, work at a WalMart project is not part of the GSA contract.
So, if the GSA contract requires an employee to work 20 hours, then you pay the prevailing wage for the 20 hours worked, and produce a separate payroll statement (or a separate line item on the employee's paystub) for the GSA, so that you are clearly separating the two jobs from each other. Then, you pay the employee their regular pay rate for the WalMart job, and identify that separately on the payroll statement.
I hope I've answered your question. Please let me know if you require further clarification. And, please provide a positive feedback rating for my answer -- otherwise, I receive nothing for my efforts in your behalf.
Thanks again for using Justanswer!