There's actually no "new evidence" rule around grounds for appeal - there's no problem with producing something that wasn't part of an appeal case in a subsequent request for review. So that won't make any difference.
Why weren't the experts involved? Well, it's worth noting that Lucy Letby hasn't lost two appeals. She's been refused permission to appeal twice, once for the initial convictions, a second time for baby K.
Shoo Lee, one of the better-known experts, was involved in the first application to appeal. Myers used him in a limited way, to critique the prosecution's reliance on his work, and not to make the argument for inadequate care. That fits with the fact that an appeal is about how the case was conducted, not a more general critique.
It's not clear at what stage all of the experts became involved, though at least one, Neena Modi, had contacted the defence during the first trial and didn't hear back. Again, I suspect that this was because introducing a new expert witness to reinforce the opinion of existing witnesses would not have been acceptable to the court or an accepted strategy for appeal.
It's unlikely that either Lee or Modi could have cleared up the insulin cases entirely, since this relies on chemical engineering. So swapping them in for existing experts would have been both impossible because of court proceedings and potentially ineffective.
The Court of Appeal determined, wrongly by my reading of their judgement, that Lee's evidence would not have been relevant even if he admitted. But this is not the evidence he has since produced for the CCRC, which is broader.
The full case review by numerous international experts is not something legal aid would have covered, and it would be difficult to argue that it bears on the conduct of either of the original trials. So the exercise could only really be undertaken pro bono, after a verdict, which is how things have happened. The court of appeal has not considered these experts' reviews of the children's death, but this does not prevent the court from considering them in the future if there is a referral from the CCRC