Germany was not a signatory.
Expecting that Japanese adhere to the 1930 LNT come late 1930s is illusory. They having no problems leaving the League of Nations already in 1933 shows how much they cared for international treaties.
Italy was also gone from the LoN by 1935, and they were not signatories of the 1937 LNT.
Thus, either of these 3 nations making a big hybrid CV is not a long shot.
We also have a thing of the treaty expiring at the end of 1936.
Germany had no interest in hybrids. She went straight to full carriers with GZ and a planned sister from 1935. Later WW2 plans revolved around full carrier conversions of cruisers or liners.
As for the Japanese, apart from the
seaplane carriers already discussed (Tones, Oyodos and Mogami) and which, as I noted, had very specific roles in the Japanese mind, they gave up on the hybrid concept around 1934 with the G6 flying deck cruiser (12,000 tons standard, 3x2 8" guns and 70 fighters) and G8 carrier-cruiser (10,050 tons standard, 1x3 + 1x2 155mm 72 aircraft) designs, until the crisis of mid-1942. Why? Because they were forced to face up to the fact that, with the commissioning of the Ryujo and the Tomozuru incident, they were attempting too much on too little displacement.
So what did they do? Built a proper aircraft carrier based on the G9 design (15,900 tons standard, 73 aircraft with a purely defensive AA armament) that in due course was delivered as Soryu (laid down Nov 1934). Even her construction was delayed by the 4th Fleet Incident of July 1935 that saw the Japanese having to reassess the strength of the warships they had built / were building. That also resulted in some redesign of her close sister, Hiryu, before she was laid down in July 1936. (See Warship 2022 "The IJN Carriers Soryu and Hiryu" and Miroslaw Skwiot "The Japanese Aircraft Carriers Soryu and Hiryu")
The Italians too seemingly never considered hybrids. Having completed a seaplane carrier, Giuseppe Miraglia based on a train ferry hull, in 1923, their thoughts turned to full carriers from 1929, then again in 1933 and again in 1935/36. The last of these projects intended to use the liner Roma. It was the plans for the Roma conversion that were resurrected in 1941, and updated which saw that hull converted to the carrier Aquila that was never completed. (See Warship 2020 "The Quest for an Italian Aircraft Carrier 1922-1929" and Warship 2021 "The Italian Aircraft Carrier Aquila")
The problem for the Italian Navy was Italian law, that while revised in 1931, still left the RA in control of Italian military aviation. It provided for "Auxiliary Aviation" for the RM with little indication of how to implement it. It also limited the tasks assigned to Auxiliary Aviation to shore based and embarked aircraft for maritime recce, "combat" functions such as fleet air defence and strike against enemy vessels were ruled out. It was only in July 1941, after Matapan, that the RA agreed to the urgent initiation of studies for an embarked aircraft with folding wings.
So for those three nations it was an exceedingly long shot for them to develop a hybrid cruiser or battleship carrier.
The USN studied various flight deck cruiser designs in the early 1930s for a flying deck cruiser only to reject them. They were resurrected again in 1939 and rejected again.
Gibbs & Cox the US Naval architects proposed a hybrid battleship for the USSR in the late 1930s and produced a number of designs, none of which were turned into metal.
Britain briefly examined a battleship carrier version of the Lion class battleship in late 1940/ 1941. The DNC considered it "very inferior" to a pure battleship with its unarmourd hangar. The Director of the Gunnery Division made an even better comment:-
"
The functions and requirements of carriers and of surface gun platforms are entirely incompatible.....the conception of these designs .....is evidently the result of an unresolved contest between a conscious acceptance of aircraft and a subconscious desire for a 1914 Fleet....these abortions are the results of a psychological maladjustment. The necessary readjustment should result from a proper re-analysis of the whole question, what would be a balanced fleet in 1945, 1950 or 1955?"
A battleship carrier, carrying a complement of defensive fighters, only made sense if available immediately in 1941 given the crisis then being faced in the Eastern Med. Of course it couldn't be, with even a conversion of an existing ship, if one could be found, taking a year or more, and longer if a new ship was laid down. The effort would have been better spent on prioritising completion of the two Implacable class carriers.
If you want to delve deeper into the world of the hybrid warship I'd recommend this title, if you can track down a copy at a reasonable price,