I'd guess there are two things to consider here :-
1) whether or not stock availability in the States and/or Canada will make this a viable or practical option. If there's no available stock then the US/Canada dealer would, I assume, probably order through the regional distributor who would order from Triumph so that's the likelihood of at least one extra process stage.
2) there's a possibility of some additional mark-up in any additional stage.
So ....... time and money?
I recommended Fowler's purely because I've had good experiences in my dealings with them. Tomspurs recommended WoT presumably for the same or a similar reason. In the final analysis it might come down to which of the two (or any other franchised main dealer) has the better service or cost option offering - that's something of a gamble for the OP with service being the high stake since cost is a relatively minor consideration thanks to the insurer's liability.
We know for sure that Fowler's can do the deal so it's probably quicker to just go directly to them and preclude any need to spend time on the web and the 'phone checking who has what and can - or can't - do this, that or t'other.
BTW, I have ABSOLUTELY NO tie to Fowlers - other than as a satisfied customer. And my only 'involvement' in this is to try to assist a fellow STriple owner who asked for a bit of assistance/advice. I've been helped out by other forum members in the past so it's payback time!