I haven't tried this yet, because it is annoying to use such a convoluted process, but this should let you revert back to 10.11.3, which never had any of these problems, at least for me:
1. Make a Time Machine backup of your disk.
2. Use TM to do a full restore of your system from a backup BEFORE you "upgraded" to 10.11.4. For reference, 10.11.4 was released on 3/21/2016, so a backup on or before that date should be okay to use.
3. Step 2 will also, unfortunately, revert all your user files to the state they were in at the old TM backup, so:
4. Now use the TM backup made in step 1 to replace ONLY your home folder.
This should give you a 10.11.3 system and all your most recent user files.
As I've stated before, this is an annoying work around. TM should have a "restore only system files" option. Apple should also stop deleting the earlier versions of the OS, or we can all learn to save things like the 10.11.0 full installer so we can revert to interim updates like 10.11.3 as needed.
It would be even better if Apple would just FIX THE PROBLEM, but they haven't done that yet.