One of the key rules in the book of war, is not to do what the enemy might suspect you to do. If I may lend some advice from RTT and TTS games I have played vs players, this advice is golden.
From the US perspective, they have a fall back position, that means that the prime US objective is survival and defence. Hence the end goal does not require elimination of the Japanese fleet, only a mitigation of its ability to score highly.
Critically this allows the US player the ability to conduct a risky strike knowing that even if it fails, there is room for manoeuvre combined with this they have the element of latent initive due to the goals of the Japanese.
From the Japanese perspective, they are committed to a single objective, strike, but not be struck. There is the danger of hubris in a successful 'first skirmish', yet this is also mitigated by an appreciation of the US latent initiative of being able to have a risky manoeuvre to allow the first blood to the opponent to allow the coups de grace.
Thus knowing that, if both players are appreciating each others views of themselves, then the Japanese player would be cautious, and the American player risky.
If you double blind that, then either could take the other stance expecting the former.
However, from the American perspective, they gain nothing from double blinding, because they are choosing to forgo a lure and/or give up the initiative This makes no sense, thus the Japanese player should conclude that the US will not make this move.
Thus from this perspective, the Japanese player should expect an American attack, and expect it to be either overwhelming or probing.
From the US player, they could reason the Japanese player could reason this, hence may opt for an overwhelming attack, since a probing attack would likely be loosing units in attrition.
Thus the Japanese player should reason; US (mostly) full strike inbound. Hence fly a strong CAP. The more tricky perspective for the Japanese position is to stick to course, or 'jink' following/pending known positioning. Since if the US engage and scout, then they know the TF composition, rough strength and otherwise have the initiative no matter what.
The key issue here is what the Japanese player knows about his positioning, and his opponents positioning. While could allow several notions;
1. Strike the US ships with a mission from another TF while it is engaging the spotted Japanese ships.
While this might be a weaker probing attack, and its fairly unknown as to the amount of assets the US player may retain and not use offensively, it has the capacity to dent the US strength strongly if conducted in force.
However it also gives the game away to other TFs in the region, and will force the US to go defensive having lost units early, this will frustrate later ruses and attacks.
2. Use spotted assets as a lure.
Knowing that the US may very likely order a strong attack on the spotted ships, one could use your assets in a supporting manner to fly more missions to CAP than the TF could muster itself. In effect laying a trap.
While I'm not sure through the rules, this would be a valid tactic to pull of, and a possibly very successful one because it allows you to shield other TFs location and deliver decisive battle.
3. Shock and Distraction.
If this is a 'minor' TF one could let it wither and die, for better positioning of the stronger assets, this nets a small amount of initiative, but also belays the US positioning allowing more scouting and a better evaluation of the US position allowing the remaining assets to be committed more efficiently.
4. Scatter and Confuse.
While this is a fairly 'high stakes' war-gaming scenario, from table top and elsewhere, the breaking up of units and general dissolution of a formation frustrates an opponents ability to score decisive strikes against you, even if it greatly weakens your assets. When the opponent is unknown, it can look like a weakness or utter failure of command and so play the opponents psychology to act rashly or to pursue.
The big downside is when they don't fall for that and defeat in detail the assets that scatter with appropriate force. What's more scattering units give scouts more ability to 'get lucky'.
So what should the commanders do? Well each will have their overall plans, which we are not privy to and they should not divulge lest our chatter give away something or general intent of the other. I would suggest they stick to such plans, and not in general get too bogged down in the various bluff and counter bluff ruses that could be deployed against them.
Why? From RTT games if you focus on double bluffing your opponent to lead local victory, there is the great danger that if they realise this, will tripple bluff you and use it against you on a much larger scale. i.e. the notion of working out your opponents strategy, in this case to play the opponent for a fool.
An appreciation of the options of the opponent is important, but your ability to gain your objective is to be clear in your own strategy and work to it, rather than letting yourself get bogged down in the tactical/operational level engagement.
Another note:
The randomness in the rules suggests that on average the player that roles better, earlier is going to have unfair advantage over the player that roles better later. While this is metagaming, allowing players to see the results of roles is fundamentally bad, because it allows them to reason along these lines for if they have the metagame or not. As GM its just better to be fair and keep a record of roles, and if the players have and issue, just produce the record at the end of the game, since then one can apply statistical analysis to see if the roles were fair and Gaussian, or biased in any way.
I watch with interes