Not sure what to do but I can relate. I had a Giordana Xcel Super with horizontals too. When I mashed on steeps the wheel would slip. It was a drag. I had to crank the quick releases so tight to keep them from slipping that I then had a very hard time releasing the QR.
I looked at a picture of that bike and it doesn't look as though the drop outs can be replaced.
Maybe its time for Ebay?