I could be wrong, but my first guess is that some applications will create files with write permissions given only to the current users. Existing group/world write permission will be kept valid. First of all test what permissions your mainstream applications use for new files. Though the average application is supposed to add write permissions to the the group as well, and that is what you want, but it is obviously missing.
Take into consideration that each user will be the main master of it's own files, and your
"Intention is for all users to have rwx access to all files in this partition"
works only ig the group permissions are rwx for the group.
I'm not sure what happens if you make all 3 users share the same user ID as well in the /etc/passwd file. That would solve the whole issue. I never tried something like that.
In the worst case run a cronjob for each of the 3 users in regular intervals to issue
chmod -R g+w /mnt/share_info
but this would be brute force and a waste of system resources.