What I think is possible, trying not to delve too far from the WI, is that its possible that there could be a 'fall back' arms limitation treaty had Washington not happened. The British delegation was sent to Washington to propose steeper cuts in naval arms than what US Secretary of State Hughes suggested.
Also the Japanese delegation, as well as the naval high command, was divided internally by those that wished to go along with the US and Britain and the militant arm. Those that favoured working with the Western Powers temporarily won out at Washington.
The two powers that could be spoilers were the Japanese and French, tho much more the latter.
If the Washington Conference had failed it is far likely that public pressure would force the calling of a second conference. One which may enact greater or lesser cuts - probably greater. Historically, the British and Americans held a second conference to hammer out the question of parity with their cruiser fleets and that failed. There is some indication that it was foiled by Churchill.
We know that the US fleet expansion program was dead before Hughes got around to calling for the Washington Conference - and nothing was going to revive it. Its more than apparent that the British had the capital and means but lacked the political capital to complete the G3s. The French lacked the monetary and industrial means to build or complete anything. The Japanese were rapidly running out of money and the Italians could barely qualify to get an invitation. So some sort of limitation agreement is bound to happen.
Why not postulate a failed Washington Naval Conference, yet a succesful successor conference? That would permit the completion of the most likely to be completed ships, which would include the Lexington and Saratoga.
On the whole, the battlecruisers Lexington and Saratoga, is teamed with their converted sisterships the carriers Constitution and Contellation, could form the nucleus of a 'fast attack force' or a 'flying squadron' in the old sense of the word.