Well, since we're on querying peculiar responses, why did you seemingly butterfly away Iraq in your answer?
I don't see much benefit for New Labour in Blair resigning in 2004, as he was reasonably close to doing - politically he was very weak then as the blowback from Iraq began to hit, and personally was in a very low period - and none whatsoever for Blair personally. I think it's possible, probably likely in fact, that he's actually regarded as worse than OTL - it'll be said that he ducked and run on Iraq, got the country into it and then flounced off a la Cameron post-referendum, that he was pushed out due to his sunken status etc. He's certainly not going to be regarded more favourably than OTL. (He's not becoming President of the Commission either given how much he wrecked his reputation in Europe over Iraq)
I don't see Brown going for a snap election when the parliament is so advanced, IOTL there was an opportunity to bank a honeymoon popularity against a reviving Tories that might not have lasted for another few years, he'd probably just let it run out until summer 2005. Without having knifed Blair he'd be coming into office in a mildly less divisive way than OTL, which would benefit.
How the 2005 election goes really depends on how much Brown's honeymoon can keep up until the following summer, and how much public anger at Iraq is drawn by Blair going. Brown obviously isn't going to pull out of Iraq, but as IOTL he will be able to benefit for it not being his call to be there in the first place. I think it's likely the Lib Dems don't do as well as OTL. Overall you could make a case for Labour doing about the same as OTL, or a little better, or even a little worse - though I think the last of these is not too likely given the state the Tories were in and Blair being turfed out. I think it's easier to get a hung parliament in OTL with some small shifts than in this one.
I think it's a very fine judgement on whether all this would discredit Blairites less, more, or just about the same as OTL. In any case I don't see it as a panacea for them.