The longest heat gun repair is probably still functioning. We'll never know. When someone gets their fix, they may not come back until the next breakdown.
@wireless: I like your idea, to touch the component while above the solder temperature. It's dangerous, but it's good. I don't think you need real pressure, just a little contact - and no sideways movement at all, of course. Usually when two bodies of molten solder touch at all, they flow together. But if there is gunky film on the surface, perhaps a reflow from temperature alone may not occur, or would require a much higher temperature. A little tap could help. I don't think constant pressure is necessary, because once you have the two sides flowing together, the solder will continue to cling to each side. Obviously if the board is severly warped then you're just beating a dead horse, so we must assume that the components are still in a salvageable condition.
There are people who do this kind of thing all the time, with a proper rework station. I wish they had taken the lead on this issue in the first place. I bet even among those guys, opinions vary on whether you tap a component or not.