Okay to have both negative and positive grounded equipment at same site(location)?
In my mind, having a positive ground and negative ground connected to
  the same main site ground just seems wrong, but is it? Would there
  really be a conflict here or not?


If you are using bridge rectifiers then you'll have a big problem with a set of rectifiers for positive ground and a set of rectifiers for negative ground: -



Shown in red is the almost-short-circuit current that will flow for positive half-cycles of the AC waveform (shown as a circle). It's the same for negative half-cycles too but through different diodes.

What springs to my mind is the use of a DC-to-DC convertor that isolates out a DC supply that is equal to your current DC supply voltage. Because it is an isolated voltage (internal switching power supply and transformer) either of its two leads can be conected to ground.