Updating today from 3.2.5 to 3.2.7, I got the infamous error with the timeout. Searching a bit on google, I found that advice to delete the file install_config.php in store. So, before deleting it, i looked at it, and saw "protocol:ftp" (if my memory serve me well). i just changed that for SFTP (I had indicated port 22, but don't remember if there was a choice between ftp/sftp), and everything went well and quickly!
Maybe it would be a good idea to offer that choice (or more clearly if it's already there, as I did not see it)