Panel/Surface mount Connectors are out there, but not stocked at the usual Big Box Stores. I've used Hubbell brand. They likely would have to be ordered through a Company that supplies Electrical Contractors.
What you're looking for is unique enough that it would have to be fabricated, of course.
See Page 30 [A-30] in the Hubbell Catalog linked here for 15 Amp Surface Mounts. 20 and 30 Amp Connectors are shown a few pages later.
Of course, great care would have to be taken in wiring any Male Connector to ensure that it never could be 'hot' with power.
Since you're supplying power daisy-chained to others, a GFI at the beginning of the 'chain' would be smart. Alternately, GFI your own Power Strip and pass 'non-GFI'ed' power back out transparently for others to use, and to GFI on their own. It is not recommended to connect multiple GFIs in series. They can false trip in such scenarios.
Hubbell Electrical Catalog