I use the one from the Cyanogen Mod site.
You can follow this howto: http://wiki.cyanogenmod.org/w/Install_CM_for_maserati
As the Droid 4 already has a great keyboard I decided it would be even better if it included all the keys.
I tried to keep the keys as close to the original ones as possible and to make the replacements easy to remember.
Similar app that I found working on my OnePlus 3 with CM13 and Windows 7 is True Mouse/KB
Google Play link here: https://play.google.com/store/apps/details?id=com.z2software.btpluginhidd
Nice! Good progress. Keep us updated. I would like to test this if it works.
I don't have any issues with the screen, but to be honest I haven't given a close attention regarding what you said.
I'll have a look in the coming days and if I find something I'll post.