Okay, I think I get it now.
Here is what I think confused me the most: Typically you would just go down the entire left-hand side in order (and this works perfectly for the majority of situations, I'm sure). But when we want to add a new download site in expectation that the original site is going to be deprecated, we need to perform the steps "out of order" with respect to the order of presentation.
Following the order as laid out, we have:
1. General Information2. Theme3. Languages-----------4. Update Information5. Files & Folders6. Registry Changes7. Update Actions----------8. Download Sites9. Build wyUpdate & Updates 9a. Build wyUpdate 9b. Build Updates10. Upload your Updates
For the very first update, you generally go straight through 1-10. Then on your next update, you generally would do 4-7, 9, 10. Normally 8 is skipped because the download sites generally do not change.
So when our download site WAS changing, we did 4-10 again, in order. It should have been 4-7, 8, 9a, 5 , 9b, 10. Or 8, 9a, 4-7, 9b, 10 would probably work just as well. (And of course, in both paths, we are adding the newly built client.wyc in Step 5.)
Hopefully my thought process was clear and can be helpful to others coming across this issue. I think my problem was a lack of knowledge about client.wyc's exact purpose. Keeping in mind that, with respect to 9b, it is just another file, then the solution becomes quite clear for me.