When I went to re-download the client installation file, Windows Defender kept deleting it, marking it as a virus. Finally by temporarily disabling "Reputation-based protection" including "SmartScreen for Microsoft Edge" (I use Chrome) and "Potentially unwanted app blocking," I was able to get into the Protection history and see that the download file had been quarantined, labelled as a "Severe" risk. I was able to restore the file from quarantine, run the installation again, and now Transmission seems to be working.
But, what happened exactly? I'm a little apprehensive that I had to temporarily disable anti-virus to get it working, and really hoping I haven't exposed myself to something unwanted.