We would like to be able to customise the service desk customer portal so that, for example, all users would first be required to search for their issue (much like on support.atlassian.com) and only then when they don't find a solution, be able to create a new ticket.

I would suggest the summary is filled in with what they have searched from.

I understand this functionality is kind of there, but
a) It would be better to search first, then create ticket, instead of going down a path to create a ticket to then see matching KB articles only to return to creating the ticket
b) it doesn't do partial word matching, so if their problem is, for example, keyboard not working, then we only get a match when "keyboard" is typed, but really we should see it when "key" is matched.