The only way strike north works is if FDR embargoes sales of scrap metal and other materials but stops short of freezing Japanese assets and embargoing oil. Only then does it become an option.
As for the British declaring war on Japan if they attacked the USSR, would they? Declaring war if the US were attacked would be a no brainer as it would make them military allies in a shooting war. The USSR though would already be at war with Germany. What would the UK gain by declaring war on Japan?
Hong Kong is gone. Singapore, Australia, New Zealand, India and all the Pacific possessions are exposed to attack. You will be forced to divert resources to a second front. To what end? To show your good pal Stalin what a dependable ally you are?
Churchill wanted to support Stalin, but I doubt he'd have opened up a brand new theater of war without having the US joining in at the same time.