I totally agree, and -- from my point of view -- you're not overthinking it at all.
I think it's an important record -- a prime, early example of jazz that doesn't try to sound American/African-American. As you say, Garrick completely embraces his English-ness. As such, I consider The Heart is a Lotus -- and similar albums like it from around the same time -- to be a BIG DEAL, an evolutionary step in the history of the music.
Winstone has talked about this quite a bit. She said that Garrick gave her "permission" to sing without an American accent, using her natural voice.
Of course, this step wasn't just one artist or one album. But I think Garrick's music is probably a perfect example of a larger trend.