"How do we contunue the war in China without losing face?"
Two steps that might have worked for them:
a) Strike south but only against Britain and the Dutch Indies.
b) Attack America as well, to neutralise the Philippines but don't attack Pearl Harbour. [Also make sure you get the dow in on time.
a) would pay big if the US stayed neutral. If it didn't you still have the US having to declare war, which will avoid much of the almost rabid hatred the US displayed as a result of the Japanese attacks. Gives much better chance of a negotiated peace later on especially if you inflict a shattering defeat early on.
This is possible in either a) or b) because, without Pearl the US will still have a battlefleet. As such they will probably centre their operations around the capital ships and may well be pressurised into trying to relieve at least Wake and Guam if not the Philippines. [Know this was not the formal naval plan which assumed a slower approach but plans have an habit of not surviving the outbreak of war].
As such there is a good chance they will be defeated in such an encounter and lose a lot of ships. Those losses will be permanent as the ships will go down in deep water rather than a shallow anchorage and it will mean heavier casualties. Especially if the war is unpopular in the US and/or there is seen to be a need for concentrating on the threat in Europe its a longish shot but the Japanese might just get the negotiated peace they want. [Would still have the problem of China and very poor relations with the west].
Even if eventually defeated, which is still most likely if the US enters the conflict, Japan is likely to get more favourable terms.
Steve