Thanks for catching this. The Stray could copy Basket Case, but his copy did nothing, in the race or in the shop.
Basket Case wasn't the only one. 10 hounds had effects he couldn't pass on: Basket Case, Busby, Big Paws, Bookends, Doug, Fleece Navidad, Marty Gale, Muddy Paws, Nosy Nell and Zoomie Twins.
I went with your second idea. The Stray now never picks those hounds, so every copy he makes does something. I didn't add +2 Treats, because he picks a new hound at the start of each race. In the shop he would still hold the last race's pick, which is hard to follow.
His copies got better, so his own bonus drops from +4 to +3 Zoom to keep him fair.
Both changes are live in the new web build now. Thanks again, keep the reports coming.