How is any user supposed to be able to work with 1000 literals? I think something seriously went wrong if you end with such a process design.

You could use a HTTP filtered value set, which would allow sorting and also filtering, this could make it less painful. I still believe you should not have to have so many values. In processes that I had to use I started hating to use them when the number of entries where larger than 10.

I do have Value Sets in Attribute Customization. Even though, you still have to pick from enumeration literals.  Our Support and Dev teams have to deal with big customer base, and we cannot make our team any smaller.

I wish there is a better way to manage it.

There is no good method in any tools if the numbers for choices are that high. One will have to somehow locate the correct one.

The HTTP filtered value provider has at least a search field and you can sort. It returns a string and not an enumeration. In 6.x I hope you can also specify that a user can not sneak just add a free string. The data can be managed in an XML on the server - even from people that don't have JazzAdmin or permission to save the process.

Another way would be to create a work item type for this kind of data and create an item for each. The search would also be possible by using the text. The attribute would then be a work item. It has also drawbacks to use this approach, because you would also always see the number.