List items: Enable edit, disable create item

I created a custom Permission Level in order to allow users to edit list items but disable Create New Item. It worked for my one test user, but as soon as I applied the custom permission level to a permission group of 75 users, none of them could edit. I had to just turn on the out-of-the-box permission level Contribute, which enables Create new item. If there is a limit on number of users in a permissions group, is there a setting to override it? For my custom permission, here are the pertinent 'List Permissions' settings I used:

<No> Add Items

<Yes> Edit Items

<Yes> View Items

<Yes> Open Items

<Yes> View Versions 

<Yes> View Application Pages