I still struggle with the thought of anyone intentionally flying 350 NM away from the vicinity of their destination. I live in Washington State, which is less than 300 miles from border to border. That's like someone who can't find Portland International Airport, so they fly all the way across Washington state to land in Vancouver BC. That might make sense for a large fast airliner, but not a 120 mph twin.
If they have any working navigational abilities, I would expect some sort of local search pattern beginning at their calculated position. If they don't have nav capabilities, I would still expect a search pattern, this time based on their best guess position. The shape of the implied search pattern associated with each scenario might be different. If a navigator was certain of their position, with a known margin of error, then the search area might be limited to that known margin of error. In that case, the assumption might be that the destination had been overlooked, so the assumption might be that the search pattern needed to be repeated. Marty's search for the RC aircraft is a good example - initial search of the area missed it (been there, done that, numerous times).
The second scenario, in which the navigator cannot determine their position, implies a search pattern that expands indefinitely, but does not repeat.
There is a hybrid scenario, in which one axis of their position is known (or confidently assumed), but the other axis is questionable. Rather than flying an expanding box pattern, this scenario implies a rectangular pattern, only flying a limited distance from the known axis, while flying increasingly long legs parallel to that axis.
None of these scenarios allow AE/FN to fly patterns that eventually lead to a 350 mile leg - they didn't have the gas. If they arrived at Gardner, it seems to me that it must have been the result of a terrible error in their DR navigation to the advanced LOP, and failure to determine even approximate position in daytime. Gardner would need to be within the 160-mile box that Gary described, implying arrival at the LOP nearly 200 miles south of Howland!