I'd be interesting in knowing what you come up with.
For years I've been doing Surbiton > Richmond Park > Putney bridge and follow the Thames to Farringdon.
Curious if you can easily link in the new greenway and or CS7. Need to mix it up a bit and find alternatives that avoid Putney bridge when the schools go back.
edit: plotted it out, saves <0.5 mile and the strava estimated ride time is basically the same. My memory of CS7 is pretty grim compared with RP + Embankment (?).