I worry that horizontal nipples will be more difficult for chicks to use, so make sure they're all getting the hang of it and are able to successfully drink from them before permanently removing other water sources.
You are very experienced at chicken keeping, more so than I am. But my experience is that if the chicks have an "easier" source they will use it. I have read dozens of threads on BYC where a user kept saying their chicks would not take to the horizontal nipples and it was resolved by removing all water sources.
I push them (to the side, not in) with their beaks so they get a drink, and repeat this process every hour or so until I see the chicks drinking on their own when I am spying on them. But i don't leave any other source available when transitioning.