We have three request types (feature, bug, support):

Which logically matches our request type configuration:
However on the requests search page does not show all three types (missing suggest improvement):

And even though our workflow has the following states:
The service desk search only shows two states (open and closed):

What is worse, the open state shows rejected items also:
Right now this is a terrible experience for my customer:
1. They can't see feature requests
2. The open list constantly reminds them of all the defects we rejected.
3. They can't filter by the states of our service requests.
How do I get the service desk to map to the request types and states we have internally (which should really be the default)?