My window is cut 5/16" passed center...what is a good material that is readily available at a hardware store to pad out the window?

Make as many layers as you wish of double-sided carpet tape, and then stick whatever strike plate material you want to use on top of that.

Are you trying to pad the window to prevent noise when the arrow hits it or make your strike plate out farther from the riser?  If the former I have used mole skin in the past. They even made it in camo for a while. To extend the strike plate do as McDave suggests or glue leather over the existing strike plate. Except for when loading the arrow your arrows should not strike the riser at all when shot. If it does your arrows are not properly spined.

Bring strike plate out from the riser

I used masking tape to tape on HD velcro rug and shot for tuning, then decided to add one more layer so taped on a patch of deer hide. When that shot right (w/ 5575s), I cut two layers (one to replace the thickness of the calf hide) of hide and the rug rest into stock shape and glued all three together with PlioBond then onto the riser with Loctite all purpose sealer (like Barge Cement) so I can remove it when I go to wider diameter woodies. And here it is:

 

They make felt pads to put under things so they don't mark up a table or counter. They are kind of thick and I used them on a metal ILF riser to bring my arrow away from the riser. They are round and have peel and stick on the back! They come in different sizes.....

They have an assortment of different thicknesses of furniture pads with, or without self adhesive.

carpet tape & leather, or Velcro works well too.

you can also find real thin sticky back felt on a 8X11' sheet too, but it doesn't hold up as well as furniture pads do.

I would glue pieces of leather to the riser. Then put my arrow rest and strike plate on over the leather.