I've had 4 Saints and my best experiences were the last two pups. In each case, I worked weekly with a trainer to teach me and the pup what we were supposed to do. One point worth mentioning is Saints are very susceptible to rewarding good behavior. These tiny train me treats worked wonders.
Lol, Grace is both fascinated by cats and scared of them, so there isn't really an issue with cats. She did attack a chicken once, so we have an opposite problem, lol (chicken was fine!).
I'm basically following the same protocol as you are, so I concur that this works - the goal is to catch when they're in that hyper aroused state and break it before they can become reactive. It requires learning dog behavior and understanding your dog.
I would still offer treats even if he isn't crazy about them - a consolation prize is better than no prize at all! These are really convenient because they're tiny and Grace loves the bacon flavor thankfully: https://www.amazon.com/gp/product/B007RLDT94/. According to my Amazon history, I've purchased them 22x, lol. They're cheap enough that you can try out the different flavors.
I stopped using treats for a while once I thought I had Grace pretty well trained, and I couldn't figure out why she was regressing. I started using treats again and she started listening better.
LOL @ Lucy listening to sit more ... such weirdos.