This may also handle the issue where the URL is too long for the web server to handle.

When creating the search url, use POST rather than GET for the form.

Then use ../query34?@action=perform_search to trigger the search. A plain query34
without action will load the search for editing. To do this will need to add the
perform_search action and make the search public is you want to share it.

Probably need javascript to change the GET for POST as well.

Also consider:

  ../query?@action=perform_search&@queryname=my+query+name

as an option to search by search name. It can search across all public queries for a matching
name. However queryname is not unique. So would need to handle that case somehow.