128-131 are the ones with the most Rangiku content, you could always watch those and skip the other 6 :P it's like a 4 episode mini-arc mostly centred on Rangiku, then 1 episode each for Hitsugaya, Ikkaku, Kon and Yumichika, then a 2 episode mini-arc for Renji.
The actual answer to what happened with the flashback fights is that the anime needed to pad for time so they inserted a couple of extra scenes. In the manga it's just the part with Kenpachi that interrupts the fight with Hollow Ichigo, which is basically Ichigo's mind conjuring up a scenario to reinforce what Hollow Ichigo was saying about him needing to reawaken his fighting instinct. The scenes with Byakuya and Kariya were added for the anime, but the idea is pretty much the same.
Oh, also, the reason the name Kariya sounded familiar is probably because of Matou Kariya, Berserker's master in Fate/Zero.
Lastly, I think the site you use flags filler, but just in case, here's a reminder that 128-137 are filler episodes that basically just exist to give Hitsugaya, Rangiku etc. a bit more screen time. They're not terrible from what I remember, but I'd probably recommend skipping them to get to the plot faster.