Okay... I feel like an idiot: I didn't realize there was a Chromium browser -- I thought there were just Chromium-based browsers (like SRWare Iron which I haven't touched in over ten years). Will check this out but to get it close to what Brave does for my useage I will need to add adblocking and a few other privacy things first (hopefully that's all supported and works).

Here: https://github.com/Eloston/ungoogled-chromium/

Yeah if you got a million CPUs to compile the darn thing!

Why? They already provide compiled binaries: https://ungoogled-software.github.io/ungoogled-chromium-bina...

Portapps build: https://portapps.io/app/ungoogled-chromium-portable/

If you're not satisfied with them, there are even more options here: https://chromium.woolyss.com/

If they blocked a browser because it has tor built in, I assume they would also block those binaries:

"IMPORTANT: These binaries are provided by anyone who are willing to build and submit them. Because these binaries are not necessarily reproducible, authenticity cannot be guaranteed. For your consideration, each download page lists the GitHub user that submitted those binaries."

Brave was most likely blocked to prevent people from using TOR to bypass their office firewall filters (e.g. on NSFW sites, etc). I'm doubtful they will be scrutinizing every single binary that happens to be on OP's workstation, though I can't say for sure what kind of office culture they have, of course.

You're intentionally led to this conclusion.