Well the UK, France and US don't want to spend money, Italy and Japan on the other hand are rather more willing, and even France (along with Italy) was willing to screw the Geneva conference. With the treaty system all five powers have to agree, or it breaks down. More importantly the five powers were quite happy to spend money on large cruiser construction programs in the late 20's, and only the Depression stopped that willingness
Basically I am assuming Japan or Italy looks at the situation in the mid 20's, realizes they are outmatched by the USN and MN respectively in large cruisers, and proposes a modification of the Treaty system to redress that imbalance, and threaten to withdraw if they don't get that
In OTL the RN were unhappy in the late 20's because they wanted to build more, lighter cruisers. And the USN and IJN were happy with fewer heavy cruisers.
In TTL the unhappiness would be the other way round.
The end result would probably be something like the 1st LNT, at about the same time, with the cruiser piece changed as the RN would hold a stronger negotiating position.
The status quo suits them, instead of the USN and IJN.
Possibly get something like:
Each signatory has a number of cruisers.
Each sub-category counts towards that number.
a) 8-10,000 tons, or any guns over 6" and up to 8". Allowed up to 2 aircraft. Counts as 1.5 cruisers.
b) 5.5-8,000 tons, all guns 6" or less. Allowed up to 1 aircraft. Counts as 1 cruiser.
c) 3-5,500 tons, all guns 5.5" or less, or less than 6 guns of 5.5 to 6". No aircraft allowed. Counts as 0.6 cruisers.
The USN and IJN could build the large cruisers they want, although fewer of them (and without putting a ridiculous number of 6" guns on any of them).
The RN, MN, and RN could build the smaller 6" cruisers they did historically.
And the old RN C&Ds, the IJN Sendai & Natori classes have there place to play as second line 0.6 cruisers (even if some do have to land a gun or 2 and replace with AA).