@stuartjb I'm not sure that When The River Runs Dry is the most CH-like H&C song. It's a great song, but the intro in particular sounds at least not stereotypically CH like. Something like Mr Bigmouth with a Neil vocal might fit right on ToLM or TA.
I have a memory that Mark Seymour released a more poppy solo album after the more H&C like King Without a Clue. Quickly looking him up on Spotify, I see that he's released a whole lot more solo albums that I knew of - I've got even more catching up to do. I can't find the album I was thinking of, but a lot of MS's solo work is somewhere in the CH ballpark. I'd have to listen more to pick out individual songs.
I'm not too familiar with Dodgy, though I recognise the song Staying Out for the Summer. I can't find "Sonny" by Welsh Dan on either Spotify or Youtube.
I'm guessing from your choices that you prefer the more upbeat CH Songs, the Locked Outs and Black and White Boys?
The thing that makes This Summer by Squeeze really CH like for me is that not only is it similar in genre and style, but also includes those little melodic/harmonic unexpected changes that Neil has said that he likes including in songs. I'm listening to Mark Seymour's "One Eyed Man" right now, and it's in the CH ballpark, but for some reason the songs sound a bit more recent solo Tim Finn than CH Neil Finn to me. Maybe "Ready to Go" could be on a CH album with a Neil vocal. But I'm guessing from your choices that you might go for "Lost in your Illusion"?
It's tempting to say that any well written sophisticated melodic song could be a CH song. I'm trying to stick to the smaller number of songs where the arrangement is such that if the vocal was switched, it could be CH. E.g. melodically and lyrically, I think that Lindsay Buckingham's song "I am waiting" could go on Intriguer, but CH would never release anything that sparse and low fi on an album, would they? https://www.youtube.com/watch?v=_FXe86mCv_w