Curunauth: Yeah, it was eating me last night after I quit so I searched some more and found that. I've got a decent set of saves with which to test it, I'll try to find the exact number.

(Also, another thing that doesn't work is specifically using Karorn, from another guide that had a very detailed method.) I am puzzled how everyone has this idea of needing a 0-XP party member when it's so easy to test . . .

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Verified in great detail:

You need 62 total strength or better. Experience does not matter, it works with 0XP chars or all level 2 and higher. PHY does not matter, you can be tired or full. Max strength doesn't appear to matter, as I failed with a 20 str character when <62 (and a 17str at 61), and succeeded with the strongest guy at 16. It does not matter at all who is in front, even a str 4 character.

Personally, my preferred party lacks the strength, so before building it I'll grab some strong throwaway guys, then let them get killed off. (Orcs in cities are so helpful for getting rid of people before recruiting new ones!)

A tip for most players: partway through the game, there are two events where you may lose most of your party (both have solutions, although the solution for one of them is inconsistent with the "hard way" solution that involves losing most party members) - this is a good time to pick up a strong temp crew. Failing that, you'll probably want to switch your initial party for some better characters once you get access to them, so you could put strong guys in the weak casters' slots, grab the sword, then replace the temps.

The east-central tavern in Urshurak city has STR 17,16,16,13, and 11 - so even with Kiriela at 4, I could easily build a 62+ throwaway party of people happy to vote for each other. The Fragonir dock-village has no orcs and a lot of guys, but many of the fighters dislike each other, and it's much further away. You only need to fight one orc group (reloading resets it, good if it's a group of 3), so even Kiriela can solo it without even needing a trick (see my city navigation post).

I've included just three screenshots, a fail at 61 and successes at 62 with no XP and at level 2+. Str: Gaarth 17, Boroman 16, Kiriela 4, Obarmon 11, Fonahir 13, Brom 16, Manatar 15.
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(orakiorob, could you quote / repost this information so I can mark it as an answer? I'd like to give you credit, but I want this information marked. Thanks!)