Going to focus only on the 3DS part for this reply, first off scratch the 18-24months part, it’ll be between. 6-10months at this rate.
3DS vs NSW Quarter Aligned
Gap is currently 1587k as of last week. 3DS sold 537k in the same quarter and NSW is aiming for well over 1mil. Gap will be under 1mil before Oct begins so gap should be anywhere between 300k-700k by end of the year. 3DS sold 638k in Q1 and NSW will beat that easily by a margin come Jan-Mar.
Only thing holding back NSW right now is stock. There is even a possibility though very small it could beat it launch aligned by dec.
Also I wouldn’t put in so much stock into japan history as NSW isn’t following any trend of hardware before it. NSW could very well do 5mil next year as well without a price cut.
Actually, you're right about the 3DS. I was eyeballing the rather steady trajectory seeing over the past three months and extrapolating from that, and as it turns out I apparently can't calculate angles for shit without actual instrumentation. After actually calculating the Switch's lead over the past 13 weeks, it's averaging about 47k/week more than the 3DS on an aligned basis for Weeks 166 to 178. With its current deficit of about 1.56M, assuming the current trajectory it should catch up to the 3DS in LTD sales in approximately 33 weeks, or late February. It may be sooner than that because of the holidays, though in October the Switch is going up against the release week of the New 3DS, which will slow down its progress a bit for a couple of weeks.
Also, nothing ever quite "follows the trends" of preceding hardware, because no two systems have the same shape to their sales curve.
For the Switch to pass the DS in Japan, it would have to be the most back-loaded system ever in Japan, and by a considerable amount. By time it hits the 3-½ year mark in early September, it will be at around 14.6-14.8M in Japan. That means in order to pass the DS it will need to sell well over 18M units to match the DS, which also means assuming it'll only have reached about 45% of its lifetime sales by the beginning September. I just don't see that happening, because no system in Japan has ever sold anywhere close to that much past the 3-½ year mark, either in absolute numerical terms or in terms of a portion of lifetime sales. The Switch would need to not simply beat past records for later-life sales, but absolutely shatter them by an insane amount, and I don't believe in postulating records like that without some damn good evidence, of which none exists.
So once again, beating the 3DS is a certainty at this point, but beating the DS is a near impossibility.