Turns out, there's a web-based system to pick/ban maps for most popular esport/competitive titles.
And it turns out they have recently added TF2.
Pretty flexible, you can fully customize pick/ban order, team names/logos and best of X. After creating your pick/ban you get a handful of links for team captains to pick/ban in real time as well as viewers' link to observe the results live. There is also an optional OBS/something else overlay if you want to include this into your stream, The UI looks kinda rough though, I can't imagine it actually being used in a serious broadcast, but I imagine that would be nice to have for scrims or small tourneys.
Shoutout to Wiethoofd who sent me this.