Although I do not consider Nolls ideas to be correct because they rely on the claim that fragments A and B are not joined properly and that the left edge of B may have extended much further, they do seem to demonstrate how easily a mistake in reconstructing this fragmentary text could occur.
It seems to me that the Jehoram and Ahaziah reconstructions are the simplest answer and also a logical answer, since we know they both died at the same time and that this occurred in the period of Hazaels reign, which also fits with the archaeological and paleographic dating.
Apparently there is only one letter missing in the gap caused by the break.
The other seven lines shared by the A and B fragments have increasing larger gaps the further they are from line 5.
The history of the city as Israelite started in the period of the Judges and continued through the period shortly before the exile by Assyria (2 century testifies to the fact that it was an Israelite city at that time or at very least not part of the then bordering Assyrian empire.
Apparently all three fragments belonged to a larger monumental inscription that had been broken in pieces and these pieces in turn were used as ordinary stones in later construction.
The fact pointed out by Biran/Naveh (45 p9) that Jehoram is the only king of Israel or Judah whose name ends with the Hebrew letters resh and mem is correct.
Since we know from the bible that both men were killed at the same time, the conclusion that the yahu ending in line 8 of B refers to Ahaziah seems very logical, especially since the only other ruler of Judah in that time period with that ending was queen Athaliah.
That evidence being that the end of line 3 most surely is continued at the beginning of line 4, as the word Israel could be guessed at even without the end of line 3.
(Indeed Biran/Naveh did guess this very thing in 1993, see 43 p92) If the obvious reading is correct, then the Stele is suggesting that its author had placed it in what had been Israelite territory, for this is contrasted with the king of Israel formerly entering the authors territory.