So I ended up taking those 4 cassettes in my shed and dismantling them to make a franken-cassette with the best sprockets I had. Made no difference. And now I have noticed that the gears used with the small chainring are also skipping a bit, but no where near as much as middle chainring.

I would like to understand what is going on here. It's almost like, when the large chainring is used, the tension is greater and the chain sits in the teeth more firmly so it doesn't slip. In the small chainring, the tension is so low that it won't slip, and in the middle chainraing, it's just enough to make it slip. Dunno.

Long and short of it is (unless I'm missing something here), all my cassettes are too far gone in gears 5-7, and I need to replace it. And in future I need to change my chain more often.