Although I can't vouch for the "safety" of this specific update in and of itself (still running 5.8.1 over here), yeah, that's the right order to do things (assuming the JB/bridge situation is golden beforehand).
A minor nitpick: you don't need to reinstall MRPI (unless you want to update it), it lives entirely in the userstore, it won't be affected by an update. (And the package folder is named "mrpackages", just to be exact for people landing on this via a search

).