I was wondering if anyone knew what the equivalent of "on that note" in Japanese would be.
I am not a native speaker, but I think I have a word that will work in this case.
In English, "on that note" essentially means "let's end there," or even "well then." It is a phrase that you use to essentially close a topic of conversation, table it for later, or to create an opening to physically leave if needed.
In my Japanese experience, a lot of people will accomplish what I listed with the simple phrase それでは, which is often shortened to では in informal circumstances. The translation listed on jisho.org is
well; then; well then; in that case and I feel that those are good translations. But it doesn't really capture the context in which it is used. Simply, it provides a final thought for the conversation (one that you are just confirming got finished), allowing you to potentially table that topic of conversation for later. It also provides an opportunity to end the conversation and physically leave if necessary.
So while not a perfect fit, I would say that それでは, or it's shortened form では provide a reasonable fit for what you are trying to accomplish with 'on that note.'