I've given this a bit of thought and would like to offer a few suggestions. However first I would also like to address the concerns of those not in favour of the points idea.
I have played other online games which have been ruined by stats, or rather, those who play for stats, so I understand why some may see it as an unnecessary distraction. It can often result in unsportsmanlike behaviour, such as to deny other players rewards rather than strive for your own. In the context of the polls here, at worst it could ammount to people being influenced as to who they vote for or include in a poll. Petty stuff, but it does happen, even if most of the time it is unintentional.
That said, I don't think it would cause any problems that don't already exist. There's enough voters for most of the comps most of the time that such anomalies are unliked to have an effect on the outcome. And needless to say, the leaderboard(s) would be in a thread of their own that everyone has the choice of opening or not.
As for how the points system would work and what it should deliver, here's a few ideas.
Seasons
It would be strongly advisable to have regular seasons, rather than an ongoing list (although that could and probably should be run as well). This would give everyone a fresh start at the beginning of each season and a chance to beat the reigning champion.
the length of the seasons is debatable, at a minimum I would say three months, though six would probably be best. A full year is too long, although the season standings could be tallied to determine an annual champ.
Points
I really think that to be fair all comps should have the same points on offer. The degree of difficulty really shouldn't have a bearing on reward, as each comp has its own challenges. Equal points will also make it fairer to determine the leader across all comps, with none giving a bias to anyone.
As for the actual points on offer, again this should be kept as simple as possible and not degenerate into a feelgood exercise where everyone needs a pat on the back. First second and thrid should get all the honours, with an acknowledment to those who made the Top 20.
1st - 10
2nd - 6
3rd - 4
poll - 1
That may seem harsh, but I think it's fair and over the course of the season it will add up. No points for HMs as simply they did not make the poll, and the HM is reward in itself.