I can't recall what the books suggested. I thought there was a Bernard conversation where a couple people speculated, but didn't come to a conclusion.
Now, if I recall, it's hard for a crafter to simultaneously use conflicting furies. Did Tavi ever get over that, or does that still apply?
In other words, wood/metal, fire/water, air/earth combos don't work. That would affect what abilities he'd have in different scenarios.
There was a good conversation in
Academ's Fury between Max and Tavi about whether or not human perception of furies made them different. The difference between nature-area furies and city ones is that in the wild areas, people were able to manifest discrete furies, like Bernard does frequently with Brutus. That's the real handicap Tavi has; he never had anything discrete, and had to do everything himself. In terms of lack of "finesse," it was described that Tavi had great strength, but wasn't able to do as many things at once as Kitai, who wasn't able to do things as strongly as he.
Being "cut off" from the source isn't enough to cancel out the abilities furies give a furycrafter; they have to be specifically countered. For example, to prevent Amara from escaping in the opening chapters of
Furies of Calderon, she's buried up to her neck in the earth. The earth prevents her from summoning Cirrus—without being able to summon him, she can't fly. But if she was surrounded by fire, for example, she can still summon him.
In short, you're right about conflicting furies; there's no getting past that. But, because Tavi has access to all of them, he'd have to be collared to lock him down completely.
That is something I can see Nic arranging. He did, after all, have access to thorn manacles to hold Harry, so I'm sure he'd be able to whip up some similar effect.
That said, Tavi takes Badass Normal to new levels. He was the only muggle in a world of superhumans, and managed to fight Canim without the use of his furies at all, and still win, not to mention the various fights against strong furycrafters that he won with skill alone.
If he's got furycrafting, I don't see any of the three main encounters going in Nic's favor. His sword would be shattered in the opening exchanges, and that's if Tavi didn't decide to simply char him to a crisp from a distance. Even when he inevitably took to the air to escape, Tavi would be able to chase him down.
If Nic managed to capture him first, as he did Harry in
Death Masks, I can absolutely see him collaring him, though, rather than keep him under running water, which would likely render all other conflicts moot.
In short, in a one-on-one fight, Tavi wins; if Nic gets the drop on him (unlikely—remember what watercrafting does for his situational awareness, and he'd sense the metal from his sword), Nic can collar him and kill him. I don't think he'd even bother trying to recruit him, either; he'd be too dangerous to keep around, unlike a poverty-stricken wizard with a host of complexes.
In chess, I give Nic the edge. Ludus is a wargame, not chess, and I think Tavi would be disappointed at the lack of a skyboard. 3D chess, on the other hand...