Likely the reason why we haven't had a long-form attempt on this and why it's confined to lists is because it's firstly extremely difficult to get him as leader, then more difficult to get him as Prime Minister, and then more difficult again to see him being in a position where he could execute most of what he wanted.
There's no magic bullet to put him into the leadership irrespective of what system is employed. As I noted above, the 1981 result in the constituencies section was based not on balloting but on activist backing. When balloting did occur, Healey did significantly better both with party members and with union members - I think he actually won in all the constituencies where balloting did occur, but it's been a while since I looked at this, but don't quote me. Of course Healey had Foot's endorsement and was an incumbent, but it does show that the left wasn't universally popular with members, as the Bennite mythology on this likes to pretend. It's notable also that Hattersley won the members section in 1983 over Meacher, in an open contest. This was probably due to the increase in balloting rather than any great shift of opinion. Though again, Hattersley had the implicit endorsement as a running mate of a leader of the left, it does show that more democracy wasn't an automatic friend of left-wing advance, and more democracy in the big elections was if anything potentially hostile to it.
But a mostly democratic franchise was very unlikely in the period we're discussing. The other two routes don't offer much of a prospect either, the MPs still having a monopoly or the undemocratic electoral college of 1981. Though the MPs were not as right-wing as Benn liked to pretend - they elected Foot in 1980 after all - they certainly were never going to elect Benn; Foot only barely won, and Foot had many qualities Benn lacked. But it's also very hard to see a route though an 'early' form electoral college like of 1981. Though the union leaders weren't the hammers of the left that they'd been in the fifties, and there was more political diversity from the right to the Bennite left, equally most of them were still to the right of Benn. So with the nigh-on certainty of the MPs and the likelihood of the unions not backing him, it's difficult to see how he could become leader.
In a vignette I once had him oust Roy Jenkins from the leadership in a TL where there was no floor-crossing over EEC entry due a French Non, and Jenkins won the leadership after Wilson lost a 74 election, and Jenkins later was deemed to have been in terrible form by Labour during a miner's strike - but even that is a huge stretch, and I'm not sure I'd replicate that outside of a vignette.
If he had become leader of course, there'd have been a split which would have made the OTL SDP look like TIG - and this is a very pressing reason why the unions would have been unlikely to countenance putting him in as leader. Even before we get into any other consideration, that alone would offer a monumental problem to the possibility of a Benn-lead party winning an election. Even IOTL, him winning the deputy leadership is generally reckoned to have been a prospect which would have lead to a huge further bleed to the SDP.
Nothing is impossible, but the prospect of Benn ever becoming leader is remote, and if he had it would have most likely been a very unfortunate episode for Labour. There would be story-telling mileage in such a timeline, though probably not from the perspective of a lot of people in this thread.
Incidentally while obviously me being Wrong About Everything here is to be expected as I fit in all the wrong boxes so am wrong by default, some people implicitly dismissing the contribution of someone reasonably apolitical like David Flin just because he's raising some unpalatable truths is pretty rude and doesn't suggest people are interested in a discussion in good faith on this.