Short of actually writing a Shift Differential rate into a T&M contract, do I have a leverage to justify adding a fee for employees that work late night shifts?

After a cursory review of the FAR, I haven't seen anything that provides specific guidance or restriction to paying a Shift Differential. Do the Labor Laws supersede it in any case? or even State?

For this example, think of a T&M contract to provide help desk support. 10 employees total with a requirement that "may have the ability to provide overnight coverage as needed". Lets say that over time the "as needed" coverage became a full time requirement.

Unclear if your question is asked as the government thinking of adding an extra term and condition for the differential or a contractor thinking about adding such a cost to a proposal. I have tried to give a quick response below that would address either.

If Federal wage requirements that would be included in the solicitation/contract do not require the shift differential why would the Government want to put in otherwise? It seems the contractors responding would decide whether they need to pay the differential so that they can obtain a workforce or to met state or local laws to perform the work and then include this cost in their pricing . If government market research suggests contractors would be paying the differential absent a specific Federal requirement it would be expected that the IGE and subsequent review of pricing should take the fact into account when determining a fair and reasonable price by the government.

If labor laws/regulations do require the differential then one would expect all contractors would be including in their costs and the government would be expected to account for through the IGE and evaluation of price.