WebTools-NG can kick off the scheduled tasks (Butler Tasks), including Deep Analysis.
I used it earlier today. I replaced a couple of movies with higher quality versions. I then launched WebTools-NG on my PC and told it to start Deep Analysis on my server. About a minute later the Plex server started deep analysis on the new files.
My server runs on Ubuntu. No idea if it works with Plex Media Server running on a Shield.