Eggie, you're leaping around more energetically than a demented frog :-D
[djeggnog to Bill] The Bible doesn't even provide specific dates when the kings of Babylon ruled, but we can rightly conclude that Nabonidus ruled for longer than just 17 years, ...
*Boing!*
If the Bible doesn't list specific dates for the Babylonian kings' rules, and doesn't even mention Nabonidus AT ALL, how can you draw any valid conclusions about Nabonidus' length of reign?
... since Belshazzar, his eldest son, was recognized in the Bible as having been the king of Babylon in 539 BC when Cyrus deposed Babylon, ...
*Boing!*
Belshazzar's mention in the Bible does squat to help you conclude anything about Belshazzar's length of co-regency nor Nabonidus' length of reign. All we know from the Bible is that Belshazzar's kingship over Babylon ended when the Medes and Persians overran the city (with no date given).
Ahh but here it comes ...
... and by our comparing the king-lists of historians along with what the Bible says, ...
Yes, you need extra-biblical sources to anchor any 'Bible dates'! But you can't have it both ways, eggie. You can't appeal to king-lists and other historical sources to bolster your preferred dates because they, in conjunction with the biblical record, establish that your preferred dates are bogus!
... it is clear that Nabonidus had to have ruled for 35 years from the year of his accession to the throne of Babylon (following Labashi-Marduk's death) until the year 539 BC (which means that Nabonidus' reign had to have begun in 575/574 BC), since Nebuchadnezzar's 43 years, Evil-Merodach's two years and Neriglassar's four years, along with Labashi-Marduk's three months, total 49 years, so that Nebuchadnezzar's first regnal year would have been 624 BC (575 BC - 49 = 624 BC).
*Boingty-boing-boing!*
Again, your BC dates and length of reign for Nabonidus are pure fantasies. I'm also curious to know why you chose Nabonidus and Belshazzar to plug that 20 year gap and not any of the other kings? In fact, there's a few 'solutions' you could have tried - all lacking historical and biblical foundation, of course, but perhaps a little more imaginative ;-)