Re: Source of the nameing conventions.
1 kajo 2 kajo 3 kajo 4 -- You say IKkyo and I say ikkajo, or ude osae or ippon dori or…..
From a quick on-line check:
Ikkyo -- first teaching
Ikkajo -- first clause
The use of Ikkajo is oft hooked up with supposed Daito ryu roots. Actually Ikkajo just refers to the first CHAPTER of the Hiden Mokuroku which include many techniques, the first being ude osae (arm pin)
In the "Secret Teachings of Self Defense" this technique is called Uchiteomote. This involves a strike first, then the standard ikkyo movement and following pin.
So, a couple of things.
Use of Kyo (teaching) took away from the ‘collected techniques' meaning of kajo which can mean bullet point or organized items from a larger work (The Hiden M.) This was probably Aikido trying to distance itself from its Daito ryu roots (which is documented) and also simplify the convoluted structure.
The ST of SD, an undocumented copy of much of the Budo Renshu has a wide range of named techniques which are rarely called that today let alone used today. (e.g. Yubiori, uchikudaki, tsubamegaeshi, uchiteura, sodetawoshi (which today would be single hand shoulder / upper arm grasp to ikkkyo), and my favorite - gansekiotoshi (not Saito's version but an elbow lock over the shoulder to a throw.)
Looking at the French manual "L'Aiki-Do La Victorire" we see the author Tadashi Abe and Jean Zin still using the kajo format in the 1950's - early 1960's edition. There are separate different techniques in each labeled ‘kajo section. Close to modern Aikido in look.
The French book "Methode d' Aikido Jiu Jitsu by Minoru Mochizuki with Jim Alcheik (mid 1950's) is set up solely by technique name followed by various attacks countered with that particular waza. Interesting is Yuki Chigae is the name used for Sankyo (3rd control). Also has a very DANGEROUS neck technique at the end which you RARELY see anymore in the Aikido curriculum. Much more dangerous than that listed under men nage (head throw) in the Cranes' tapes and book.
So it seems, there was some carryover of names from the old Daito ryu (which also listed a large number as only numbers) but also a wide range of grouping. The Nidai had to contend with instructors that had studied under his father while he still taught Daito ryu. It must have been a concerted effort to standardize format and nomenclature and safety like Kano of Judo to help introduce this initially small art to the western world.