I think it's pretty clear the reason that past Jacob didn't go this route, other than the possible paradox that is.
Pettigrew has a time turner and he is currently unaware that we have a time turner. If we go back and try to stop him and don't immediately disable him then Pettigrew will go back and then we go back and then he goes back and so on and it'll eventually come to who has more time in their time turner (I believe there's six hours?) and I'm not sure I want to bet on him having less seeing as he has an "earlier" iteration of the turner and we've already spent three hours.
Also trying to take him out without killing him while he still has a turner is a huge gamble, doable, we do have 5 echoes being used after all, but stil a massive gamble with a big pay off.
But then the question becomes, if we do that, how do we form a stable loop after we've attacked him?
The main way I can think that we could do to make that work is to fuck him up and then force him into a pact to act as we saw on the map. Something like we agree not to kill him, while he agrees to lead Lupin to the shack and then turn himself into the authorities. Though I think that might be a bit ruthless for our wand.
I'm kinda torn right now because a time war is so damn cool and I can see a way to make it work out, I'm just not sure it's worth the risk.