Yeah, I would add the capture of India, reinforcing German-held Caucasus, and recapture of Africa from the Allies, also capturing Australia, New Guinea, New Zealand, other things like that. Those are pretty standard goals for KGF.
There’s three things I usually do with the American fleet at Pearl.
1. Attack with sub, destroyer, fighters, bomber. Sub and destroyer are fodder. Fighters land on Jap carriers at the Solomons. Bomber goes back to Japan.
2. Ignore it, if I can destroy the entire UK navy in the Indian Ocean and ALSO kill off 6 Russian infantry at Burytia.
3. Send everything. I really don’t like this, because using the transport off Japan slows Japanese progress in Asia.
UK assets at India can be used for a few different purposes. One is to recapture Anglo-Egypt. Another is to reinforce the Pearl Harbor fleet while weakening the Jap fleet (UK sub and fighter vs Jap Solomon sub; UK fighter lands on US carrier). Yet another is to poke at the Jap fleet and threaten more (UK fleet attacks Jap Kwangtung transport, UK fighter lands on Burytia with the 6 Russian infantry, UK bomber flies west, threatening UK attack on Jap navy next turn.