Is extending the election of leaders beyond the parliamentary factions of parties, a uniquely left-wing position?
In this period? Pretty much. The starting position of the right was that they wanted the election to remain with the PLP, and then when this became an unviable position, which it soon did for obvious reasons, create a pure OMOV system. The left did not want a pure OMOV system, as they were interested in furthering the power of the constituency activists and the unions, which were correctly seen to be highly sympathetic to the left. The right believed the same about the PLP and the membership more broadly. Tony Benn rhapsodically praised the outcome of the Wembley Conference, where the unions voted themselves a larger portion of the electoral college than had been proposed and agreed on by the leadership, as "marvellous".
I think you're strongly overstating the case in depicting SDPers as proto-New Labourite outriders who had "long" wanted to break the link with the unions, btw.
So if not Kinnock, then who? I really can't see Shore doing it, and the unions are going to have the same objection to him that they had to all "middle-class intellectuals" (the same thing that made them distrust Hattersley, though less because of his own background and more because he'd embraced roles as first Crosland's protege and then Jenkins' vicar-on-Earth). Doubly-so for Silkin. Robin Cook, then?
But there was someone from the right of the party who would have passed muster with the unions, and indeed with the soft left: John Smith.
I don't see why Shore can't do it, in the abscence of better candidates. He's probably the only senior candidate who could appeal cross-party. (He didn't have the left cred he did under Wilson by this point, but factional heritage counted for a lot in Labour) Crucially, it wouldn't be a blowout like Kinnock, though. I can see Heffer doing an awful lot better here than IOTL. He could perfectly concievably win if he manages to win over the unions early, over Shore.
I don't see Hattersley standing aside for Smith, even assuming Smith would be prepared to stand against Hattersley, which he almost certainly wouldn't. (He was Hattersley's campaign manager, and 100% behind the more senior man's candidacy) Although he was always comfortable towards the unions, this was before his long stint in shadow economic portfolios through the eighties, so he would have been more of an unknown quantity than he was when he ran for leader in OTL; and by that point of course, the hard left was dead and the soft left no longer factionally in the ascendancy in the party. I don't see his candidacy being viable at this point.