I haven't seen this mentioned here before, but some contenders for highest milepost numbers in the Lower 48 might be in North Dakota, where 900s seem to be used for some (but not all?) business routes. I saw a few, including this one on old US 85 heading into Watford City:
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fi.imgur.com%2FndnlMxm.png&hash=f984bcb558a014d569fee976bc943009df15610d)
I can't seem to figure out the rhyme or reason behind the numbers, since old 85 isn't 56 miles long, unless maybe all business routes for all highways statewide use the same series of 900 numbers?
All routes that are duplicate numbers (mostly business and other bannered routes) have mileposts in the 900-s to distinguish them from the ordinary route. For instance, that 85 BUS starts at 950 (so it's about 6 miles long).
Here's a map if you're interested: https://www.dot.nd.gov/docs/maps/state/2015CDRS_Combined.pdf (https://www.dot.nd.gov/docs/maps/state/2015CDRS_Combined.pdf)
Some routes have cumulative numbering for their alternate routes, like I-94 (BUS 94 in Medora goes from 900 to 903, then BUS 94 in Dickinson starts at 903, etc.), while others just have their bannered routes start at nice numbers (920, 940). This leads to some interesting roadgeek things. For instance, ND maintains some service road west of Fargo as unsigned ND 10. Since for some reason they consider that the main "10" route, US 10 starts at milepost 932.6 (the milepost of BUS 94 for Fargo).
If you follow mileposts, Bismarck-Mandan has three BUS 94's and a BUS 83. However, what the mileposts say and what's posted in the field (one BUS 94) are often very different.
North Dakota is kinda odd... must be the horrible winters.
Helpful info and, yes, kinda weird. Thanks!