I've improved the installer behaviour:
Issue 2381 – Restoring ability to restart Explorer to allow upgrade of drag&drop shell extension, when installing for current user, as after-restart replacement is not possible without Administrator privileges

Thanks! I was afraid to uninstall it for fear I'd be unable to reinstall, so I tried half your solution: installing as administrator. That worked. Problem solved.

Ok, so the last option is to uninstall (keeping settings), restart and reinstall.
If you install WinsCP for all users (as Administrator), you should not have this problem again in the future.

Thanks – tried that, same result.

Ok, so please try restarting your computer and running the installer as the very first thing afterwards.

Sorry, I don't know how to do what you're asking. The only way I know of to run the installer is to double-click on the "WinSCP-6.5.1-Setup.exe" file. I'd be grateful for step-by-step instructions to do what you're suggesting.

Please run the installer with /log=C:\some\path\installer.log commandline parameter and post the log here.
https://winscp.net/eng/docs/installation#automating

In trying to upgrade to version 6.5.1, I keep getting an error. I've tried installing immediately after rebooting, but it still occurs. I've attached a screenshot of the error message. Any suggestions?
Thanks!