Yes, The Strings in Shinagawa is closer to HND. The IC Tokyo is 20.3 km from HND Terminal 3 and by car it can be reached by car from HND in as little as 24 minutes during the day at non-rush hour periods. On my recent trip, I took the Keikyu Line/Asakusa Line from HND to Shimbashi Station and a cab the rest of the way to Akasaka. Travel from HND to the IC Tokyo took probably the same time or less than the 40 minutes from Tokyo Bay. For my business travel needs, I find the Akasaka location of the IC Tokyo much more convenient and centrally located, and a 10-20 minute difference in one way ground travel compared to the other IC locations in Tokyo isn't that significant. Of course, if your business is in the Shinagawa area, than The Strings does sound like a good choice.
FWIW, if you're including the convenient pre-pandemic Airport Limousine Bus as public transit, they have suspended service until further notice between both HND and NRT to the Tokyo IC hotels. Now that Japan is expected to open up on October 11th, maybe this convenient bus service will be restored to one or more of the Tokyo IC locations from HND and/or NRT.