Well, exactly! On the basis that Israel will have proposed or sanctioned Blair, and he has special knowledge, it would be appropriate for him to act as Israel's representative or go between perhaps.
We have two distinct sides here, the only possibility of stopping attacks from both sides in the future is for the people of both sides to be completely on board - that will happen if one of Palestine's backers together with a representative of Palestine negotiate for Palestinian interests. That is the way effective negotiation works. It would need to be a proper negotiation, working out what would be fair, reasonable, lasting, workable, facilitated and supported by other world leaders.
If Blair is to be titular at the helm only, then perhaps a joint appointment of such with one of Palestine's backers might be more diplomatic.
I think your view that this is all to do with getting a genuine two state solution is somewhat naive, but let's hope. I think you are underestimating just how appalling most people think the wmd disaster was, and Blair was not only in the centre of it, but has come out with polarised statements on world affairs since. So a curious choice.