Is there a way to make a custom transaction type without a GL impact? Like something that could hold custom budget information?

Yes. I've been playing around with this from time to time

Under the Statuses subtab of the Custom Transaction Type, there is a Posting box.

Make sure the "posting" is unchecked. and use a standard custom transaction (i.e. the JE like one)

That worked great, thanks 👍. Interesting point about it needing to balance. I'm thinking I'll just put it to some unused/dummy account, which shouldn't really matter since it's non-posting.