Try to block unneeded admin menu items using “Admin menu blocking” add-on.

Btw., I work on add custom taxonomies to the code executed for the URE’s option
“Force custom post types to use their own capabilities”. This will replace ‘edit_posts’ for such taxonomies with ‘assign__terms’ capability. So you will not need to add ‘edit_posts’ for custom post types. I plan to add this to the next udpate.