No, you wouldn't be able to make any projected coordinate system with "degrees" as the linear unit, unless you made a custom unit. In equidistant cylindrical, for a equal-length box of degree intervals (like 10x10), the north-south distance should be larger than the east-west. I wonder if the data is in pseudo-plate carree. That is, it is in decimal degrees and should be defined with a geographic coordinate system, which are being treated as if they're linear.
Melita