Saguaro doesn’t seem to see much backcountry traffic, so the blanket permit idea would probably be workable. They’re not like Glacier, which is a royal pain, made worse by rangers who can’t believe anyone can hike 20 mile days. Grand Canyon NP is a different story, too.
In North Cascades NP, where I was caught last year by a ranger without a permit, they were really helpful and field-issued me a permit by radio. I explained to the ranger that the only way to get walk-in permit was by detouring to an office about 30 miles off the PNT, and if walking in from the East, the last town is 170 miles away making scheduling by fax difficult. The ranger said their enforcement is not very tough on exact times and places. If you have a permit for roughly the time and place you’re in there, you’ll be fine. I guess that’s basically a blanket permit for thru hikers. It’s not like they see very many up there.
It would be cool if Saguaro adopts that kind of policy. Now that the AZT is a NST, and there’s about to be a real trail, it may happen.
Garlic