How do I get and set specific UV values on a polygon?

Use the PolyMoveUV command. A good way to use this command is in conjunction with setAttr statements.

To see how MEL implements this, create a polyPlane, then pick some polyUV’s on that plane. Select the plane then open the UV Editor. This shows us the UV coordinates for the selected object. With the PolyUV(s) still selected, select Modify > Transformation Tools > Move Tool from the Maya tool box then use the manipulators displayed in the UV Editor to see what MEL commands get written to the Script Editor window. Generally, the output looks something like:

setAttr "polyMoveUV5.translate" -type double2 0 -0.1187236 ;

You can set or store the outputs using normal arrays.