I like BIN as it sands really well, you can wetsand it like automotive primer almost after being on a day. Just sands mirror smooth. I think if he did two coats and used it as a filler/sanding primer it would look awesome, but he still has a possibly failing coating underneath. I've used Breakthrough and Advance and would say Advance is definitely more oil like, but Breakthrough isn't bad. Breakthrough would feel like a better version (much better version) of Proclassic, Advance would feel/look more close to oil. Since it's a 50s house and they're wanting to go for something retro by keeping the cabinets, Advance might just "fit" better in terms of finished feel. I'd also try to go satin vs gloss to hide some imperfections, too. On the original paint job you can even see some stipple/etc that I don't think you'd get with modern paint and even a microfiber cover, so you might actually need something like Bondo glazing putty over some spots to skimcoat it out, if you're not going to bare wood.