We can work around this by always doing a POST call. A modern browser will use history.replaceState to make the URL unique if it is less than the allowed limit.
Following the steps above, but using the production server instead, I get a proxy timeout error in step 2, reported in Bug 1019072. Note that Bug 756082 has well over 1000 bugs in its Depends On list. I remain skeptical that that is a sensible way to use Bugzilla (or any bug tracker for that matter). If one wants to track the high priority bugs for a release, I would have thought a better way to do that would be by setting appropriate values for the priority field and an appropriate release flag and crafting the correct query to retrieve the list of bugs that are thus marked as priority items. Using tracking bugs like Bug 756082 to keep a list of priority issues is error-prone because it relies on users to remember to add dependencies and important bugs could easily be missed.
The procedure in Comment #0 works fine now on the production server (takes about 10 seconds to "View as Bug List"). Presumably fixed by the same upstream changes as fixed Bug 1019072.