If I can offer some help Re: some of the companies..
K was based first in Cork City and was the company responsible taking part in the burning of Cork. It was moved to Dunmanway and billeted at the Dunmanway Union. After a series of incidents it was wound down with a proportion of the men transferring to N company which was based in Trim, Co Meath. Most I believe were transferred to K company, which took over at Dunmanway.
I see Cottrell lists D as based in Dublin - not so. The company was based in Galway city. An early company was Lt Col Guard (he may have been the second as I think Crozier replaced the first). Guard had a v distinguished record in WW1 and beyond. After command of D co, he was promoted to 2i/c of ADRIC, serving under the previous incumbent Brig Gen Wood who took over as Cmdt on Crozier's departure.
I have an idea that I was based in Dublin certainly for some of the time and may have a report to that effect. One of its commanders was Adrian Hulse who was c5'6" and weighed c 15 stone. Don't suppose he leapt over too many walls in full kit!
NB Q company is a curiosity. Set up c April to police the North Wall docks against arms smuggling, it had a higher proportion of cadets who had not held commissions including some from the merchant marine. In other words ADRIC wasn't as socially exclusive as supposed and placed value on technical expertise
Hello Old Owl
On joining the Auxiliary Division, recruits were given Aux. Div. numbers starting at no.1 in the order that they joined. It would appear that they were given 5 digit RIC numbers as well. In the Aux. Div. register at Kew (H.O.184 - 50/51) the first recruit, no.1 received the RIC no. 72096 as well. This practice in the register was terminated at no. 72595, allocated to Aux. recruit no. 237. To find RIC numbers higher than that, allocated to Aux. Div. members, one would need to consult the separate RIC personnel records.
The list from Peter Cottrell's book posted by Mark, has a few blanks, and "I" is not the only company missing from the list. Other compamies missing are "K", "N", and "P". Mark's posting is to be commended for making more information available, on a subject that frankly, is difficult to research. There is no doubt that your man belongs in "I" Company.