Common karate wisdom has it that Jitte/jutte means ten hands (implying strength of 5 men perhaps or ten onehanded men ), Jion means temple sound/bell and Jiin means temple ground but I believe the verifiable meaning is unclear because the characters used nowadays to write the name of the kata are not necessarily the ones used originally. The "monk" connection may be spurious. "Ji" I think means mercy or somthing similar and supposedly there are many temples with names such as Jion in Japan. Maybe it just refers to a distant relationship to Shorin/Shaolin martial arts. I will have to look in the Bubishi to remind myself if any of these are referenced as Chinese forms originally.
There are certainly obvious similarities between the three, including the fist in the hand at the start, mirrored movements start Jion and Jiin, three palm strikes (3 shuto in Jiin/3 tetsui strikes in Jiin and Jion, latter with stamping kick, stamp in Jitte with high almost tetsui movements), manji-ukes and age-ukes in all three but also techniques common to only one kata (double fist techniques end of Jion, possible bo grabbing techniques in Jitte, wedge blocks etc in kiba dachi end of Jiin). All three always felt similar in practice and the embusen are very similar as well. I have read that some people think Jiin and Jion are variations of the same kata or alternatively that these three kata make up a separate system but who knows...
How could we ever really find the origin unless you discovered a Chinese group previously unknown using identical forms? Does it matter (although it may be interesting), if we are still able to find practical applications for the movements?