Parsing the above, it seems like the recommended choices are

Hyatt Place
Courtyard
Sofitel
HEX if you can get an award

I will be arriving T3 at 9am and departing flight the next day T5 at 5pm. I will do a combination of recovering from jet lag (crappy arrival time from the LA, won't be getting much sleep on the plan) and a little sightseeing - might have time for Windsor Castle or Kew Gardens.

The major advantage of the Hyatt Place to me is early check-in (plus stay credit).
It seems like the convenience of the Sofitel plus nicer rooms might be worth maybe $80 extra (to me) - one less segment to deal with after returning from kew..
Courtyard seems to be in the middle in terms of hard product.

How much is cab/uber to Hyatt Place? I am unfamiliar with Bolt. (We don't have mobility issues but will have two large and two carryon bags to deal with (for the two of us). If it saves 15 minutes and lugging luggage, might be worth it.),