From the photo it looks like you have vertical drop outs - please correct me if I am wrong - and ignore the rest of this post :-)

If this were the case making the drop out slot deeper on one side or packing out the other would change the vertical alignment of the wheel and would not affect how it centres between the chainstays.

You would have to alter the sides of the slot which would then be wider than the axle so the wheel could move about whilst riding, unless the skewer is done up real tight.

Might be better to find some suitable sized thin wall tube to fit over the axle where it fits into the drop out and then widen the drop outs such that the wheel fits and centres - it is a one way trip though so have to get it right first time.