If you have the room for it and don’t already, you should see if you can get a shock mount for the mic if you can’t put it on a boom. It would make a big difference for those vibrations!

I use a keychron at work and it’s very good for the price. Not a heap to choose from in the 100% range but all very reasonably priced. If you’re after serious quietness you probably want linear switches but these are often pretty polarising to people. There’s no tactile click at all when you’ve activated the key. You might be surprised what you can get away with on VC though, I use a condenser mic and a keyboard with blue keys and generally have no problems with people hearing it. Good mic positioning on a boom helps a lot, and some new noise cancelling technologies are pretty excellent at blocking clicks. With a headset mic it would be really unlikely to be heard.