I really don't believe in the irreparable thing. Especially since both cats are young, and they don't have a long history with each other. I think pretty much any sort of "mistake" made in cat introductions can be rectified with some effort and patience.
To me the biting is the most worrisome thing. You should definitely try to get a video of the biting. That would be really instructional, both for you and for others who are trying to help. You mentioned that in at least one case it was a "butt scratch" that got you bitten. That is an area that not all cats like to have touched. Also I think you should be mindful that there may be sensitive areas on your cat. If others are right and it's an over-stimulation thing, then don't do any full body strokes. Only a few touches around the head/neck/chin, and maybe back off if she gets real purry.
I do think it's a mistake to spend most of your time with the new cat. It's really the resident cat that you have to mend fences with when you get a new cat. I would shoot for 50-50 in terms of time spent, but err on the side of spending more time with the resident cat.
I can understand why someone might make a generality about the running thing, but I think that's certainly over-stated. I think in general if one cat runs from another cat pretty consistently, then it's the hunter/prey relationship. Cats really can't seem to help themselves when another animal scurries away from them. So an alpha/beta sort of order is certainly being established. But that said, that doesn't mean it "won't work out". There's a number of My Cat From Hell episodes where they work that sort of thing out. And his solution to the situation isn't to try to scold or prevent the alpha beating up on the beta, it's working with the beta to not be so afraid of the alpha. Basically, it's "if the scardy-cat doesn't run, then the whole episode is averted" type of idea.
But you may have to accept the possibility that there are different levels of "things working out", and it may be that the two cats are not best buddies, and do occasionally clash, but generally tolerate each other fine. Two of my cats, Serafina and Neytiri have that sort of relationship. Every few days I'll hear some "grumbling" (sort of half-hearted growling/hissing), followed by a full-speed chase where Serafina (my bengal) chases Neytiri (my oriental). And Serafina is in full hunt-mode, and Neytiri is in full flight mode. But since there are always plenty of escape routes, and things to hide under or climb, the chase is usually pretty short-lived, Neytiri finds an easily defensible position, and the game ceases to be fun for Serafina, and then an hour later it's like it never happened. Both of them accept each other as roomates, and have no problem with each other's presence.
_________________ The little monsters 3
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