I should clarify that JW literature does claim that Jehoram's 12th (final) year was 905BCE rather than 906BCE. It is therefore implied (but not stated) that his 'first' year in 917BCE was an uncounted 'accession year'. However, that 'excuse' does not work because any such accession period transitioning from Ahaziah (of Israel) to Jehoram would have been during the final year of Ahaziah (of Israel), which JWs place in 918BCE (plus, JWs claim that Ahaziah's reign was 'credited' to Jehoram as of 919BCE, further negating the likelihood of a separate accession period). Without calling 917BCE an 'accession year', that gives Jehoram a sole reign of 13 years if 905BCE is taken as his final year. That would mean that 'reconciling' the reign of Jehu in this manner would simply move the extra year back into the reign of Jehoram instead.
I should also add that in addition to the way the reigns are given in my chart, there is another scenario that is compatible with the reigns of Ahaziah (of Judah), Athaliah, Jehoram (of Israel), Ahaziah (of Israel) & Jehu. That is that Ahaziah (of Judah) may have started his reign near the end of Jehoram's 11th year, such that it could be given as that year or rounded off to beginning in his 12th year. In this scenario, Athaliah and Jehu would still both begin to reign prior to Tishri of 840BCE.
If Jehoram (of Israel) began his reign between Tishri & Adar (approx. October to March), it would then be possible that Ahaziah (of Judah) began his reign between Nisan & Elul (approx. April to September) of 840BCE (instead of late 841 to early 840BCE). In such a scenario, Athaliah's reign would still begin prior to Tishri of 840BCE. However, comparison of the transition from Ahaziah (of Israel) to Jehoram with the reigns of Jehoshaphat and Jehoram (of Judah) does not suggest that to be the case.