Hi Tory
Freydank, in his 1991 book, listed all the Middle Assyrian limu dated letters that he had access to in the Berlin Vorderasiatisches Museum. Amongst the royal limus, half the time they have no title and half the time they are titled šarru or uklu. Here is a list of the relevant VAT numbers
KING WITH TITLE WITHOUT TITLE
Ellil-nirari 20230
Tukulti-Ninurta 19628 20166 20220 20333 15379 19828 19882 20222
Aššur-nadin-apli 18095 20054
Ellil-kudurri-uṣur 20165
Ninurta-apil-Ekur 19922
Aššur-reša-iši 20289 20327
Tukulti-apil-Ešarra 19964 19980 19987 20159 20218 15490 19487 19961 20249
I prefer my arrangement for Aššur-nadin-apli as it retains a 3 year reign for him as per the main King Lists, that is 4 limus - from his accession year to the year of his death, three year later.
Regards Joe