Yes, there will be, for the reason explained by the math I posted.
What's the groundspeed before the turn? -499
What's the groundspeed after the turn? 501
The difference is 1000.
I read your post again, and it still rearranges the terms in error. Look at scenario A, and see that obviously everything is right. This is common sense to a private pilot. And then look at how every element translates to scenario B. Have I made any mistakes in the translations?