Given the criteria you've described, don't think that there is a tool that does exactly what is desired.
But, it might be possible (with limited automation) with a combination of a Moodle server dedicated to serving out LTI resources ... *each* activity/resource being setup as an individual LTI tool that could be linked to by the other Moodles. That's *each* ... individually. That's kinda mega LTI Moodle server administration.
A message could be distributed via forum on the LTI Moodle to which all teachers in other Moodles are subscribed that a new resource is a available. Information provided in the posting for linking information as well as description/screen shots? Teachers, then, have an the option to add to their course but must do so manually.
OR ... again mega admin on the LTI Moodle ... the LTI Admin could make a backup of the course containing the 'shared' activities and the backup would consist of only that new resource. A link for the backup provided the teacher. Teacher could download the backup, restore it to their course.
If one were to really get gu-ruish ... the LTI Moodle could make those backups via Moosh and put those into a 'unirepo' file system which is mounted on all the other Moodles. Teachers then on the other Moodles could restore those single activity backups without having to download then turn around and upload ... they simply use the file system repo on their server to restore that single activiity backup ... again ... mega Moodle admin.
No ... haven't done the above so am certain one will find some 'catch 22's'. :\
'spirit of sharing', Ken
