A comment from Jacques (I've only corrected some typos). He thinks the first two units (Akizuki and Teruzuki) are to be delayed a while compared to Mark's proposal (Solomons 19-30 September 1942 & Solomons 1-31 October 1942).
In OTL the Akizuki class was ordered in two batches (6 ships in 1939 and 10 in 1941) and the lead ship was launched on July 7th, 1941 and completed in June 1942. The second ship, Teruzuki, was launched on November 21st, 1941.
If we admit that the Kondo report is to push the IJN to significantly improve AA defence it could be possible to have a decision taken between January 15th and January 31st, 1942 to modify the Akizuki class by fitting German close range AA weapons (37-mm) and AA directors.
Admitting Japan is to get its first 37-mm gun (with production drawings) early January, this would entail some redesign of the ship. (possible deletion of the quad 24' TT and fitting of three twin-37-mm mountings - one aft and two on the beams, staggered - and two triple 25-mm and 4 single 25-mm, with a German-type AA DCT aft and the prototype installation of the FFO Mk2 Mod3 radar similar to the German FuMo 24 with a 6m x 2m manually rotated antenna giving a 15nm range on ships and a 25nm range on medium-sized aircraft at 5,000m altitude. This set was mostly developed for destroyers and cruisers).
Even if discounting the Japanese trend to go for excess modification, changes in the secondary armament and the fitting of new electronics and a stabilized AA fire-control systems are to delay completion by probably 2 months.
Being the lead ship of not just a new class of DD but a new concept (the DDAA) one can expect that Akizuki, even if completed by late August 1942, is to be submitted to thorough and complete testing in home waters to assess her actual capabilities. Remember that the class main armament is also new. The whole book on the ship is to be written.
This implies Akizuki and Teruzuki to stay in home waters at least till late November, exercising alone or in company. Then both ships would need a rest and R&R.They would reasonably depart from home waters by late December 1942 at the every best, reaching the combined Fleet by early January 1943 and are not to join operations before late January/early February.
Even if their 100-mm guns are to be less effective than US 5'/38 (and the more so because Japan is to be unable to develop proximity fuze) both ships are to make some impression on Allied aircrews attacking the Combined Fleet and for a time they are to be confused with light AA cruisers on the RN modified "C" class cruiser pattern.

