I've made a couple of scripts for this as I keep needing it for various projects.
These work with the standard desktop and with the chrome browser as I use it for kiosk mode.
The main problem I had was making the file system RO only to realize I needed to install/update something so I've included a script to re-enable RW mode.
Nothing complicated, but they seem to work reliably.
One caviat, if you riu the makerw script when the file system is already RW you'll screw up your OS, I should add a check at the start of the script really...
https://github.com/MarkDurbin104/rPi-ReadOnly