I think we often follow the same route (though at radically different times).
It sounds likely.
If I'm in a hurry I sometimes just take the A24 all the way to Croydon, but the back route (LCN 5 if I recall) is a bit (ok, lot) more relaxing. Though the bit after Norbury is (or was horrible) – Norbury Avenue (and the streets between Thornton Heath and Broad Green) tended to be a rat run, narrow and over parked, the usual story with impatient drivers who can't wait a few seconds for a place to pass safely.
Not seen the improvements though, will have to try on my next commute.
I think you mean the A23, the A24 will take you towards Leatherhead, not particular close to Croydon.
The Norbury Avenue direction doesn't work for me, it takes me away from my destination, but I did use it a few times when I first moved to Croydon, partially as an experiment, and because I was helping take a group of novice cyclists through there, back when Hovis was sponsoring the summer cycling closure in central London. I found it fairly horrible, and as you say, met some very nasty aggressive drivers. After Thornton Heath Pond, I use London Road (A235) into Croydon, since it's largely better than the Thornton Road/Purley Way, with its own horrible junctions (Lombard Roundabout and Ikea).
I believe that Norbury Avenue did have some closures placed in it, to stop through traffic, but still allow cyclists through, but I believe that was an experiment, and has since been removed.
I only use the back roads between Tooting Bec Common and Norbury southbound, because two junctions near Streatham are verging on being lethal in that direction. Northbound, whilst the A23 is busy, it's surprisingly safe for cycling, and you do see quite a lot of cyclists on it.