I drove up to Montana last weekend on US 93 and noticed something fun:
US 93/Montana 43 in 2014 - ITD-spec control city sign (with an MDT-spec "Big Hole National Battlefield" sign underneath it):
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fwww.corcohighways.org%2Fhighways%2Fid%2F93%2F28tomt%2F22.jpg&hash=bb68742fde5cf769603f1724dacb63b9fd6c1a4d)
US 93/Montana 43 in 2015 (courtesy Google) - newer ITD-spec control city sign:
https://goo.gl/maps/jdDQx2FWYTGqrmge6
US 93/Montana 43 in 2020 - MDT spec control city sign:
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fwww.corcohighways.org%2Fhighways%2Fid%2F93%2F28tomt%2F22new.jpg&hash=ca340118057e4abf93272da02c553ca504fb21ab)
So this sign was replaced twice in five years, first by ITD and then by MDT. Any other known instances of states seemingly (and probably unknowingly) fighting over who has jurisdiction of a given road sign by replacing perfectly good, new signs from the other jurisdiction?
Not exactly what you're going for, but, I thought it would somewhat fit here. When Ohio resurfaced US-30 from the Indiana/Ohio state line eastward, they posted their variable speed limit signs one mile in advance into Indiana. During a lane closure, if there were workers present the speed limit was posted at 55. But when there weren't any workers, the limit would be posted at 65. In Indiana. Where the speed limit is 60. So in essence, the speed limit went UP in Indiana from 60-65 mph for the work zone.