No documents available make a case for #51406 as having been a UP car.
Now let me ramble on here.... I tend to ;-)
UP classes B-50-7, -8, -9, -10 are a mystery and if anyone has information about them would be grateful to be enlightened.
In the ORER every six months starting 1-1913 through 1-1916 and then 14-1920 well into the renumbering there is no series that would include #51406. It is possible to look at every month in that span on Google books but my quick look is not encouraging.
I also reviewed the service data I have compiled from the original Union Pacific equipment records made available by Don Strack. In the 310 series series built before 1945 or renumbered from those series there are no UP or subsidiary box cars series that would include #51406 (1728 pages). Indeed, there are no B-50-8 cars at all. B-50-6 double-sheathed cars were built up through the end of 1913 and the next series are B-50-11, also double-sheathed, built 1914. The intermediate classes may only have been engineering proposals or resulted only in a sample car; I've not encountered documentation for these possibilities. UP began building fifty-foot single-sheathed auto cars in 1913 but they are too long to match the car in the museum and at any rate also did not have series that would include #51406. The fantastic primary documents behind this of which you are probably aware are available at:
As you note, the SP B-50-8 cars match the museum car in side truss design and single-sheathed end pattern. So far I am unaware of any that were renumbered into 51xxx series as box cars. In the 1940's however, some were among several classes reconfigured for wood chip service in series 51xxx-52xxx. There may lie a tale which needs to be told by someone with knowledge of the SP wood chip cars.