Amtrak's platform is not next to Omaha Union Station, now the Durham Museum.
Amtrak stops beside the former Burlington Station and uses the Burlington Station's platform. The Burlington Station itself stood derelict for many years, but has now been rehabbed and is the home of an Omaha television station, but with no public access.
The pedestrian overpass over the UP and Burlington tracks (now BNSF) between the two stations, Union and Burlington, has been gone for decades.
Operationally, switching over to UP to serve the Durham Museum would be problematic, assuming the Durham Museum even retained any platforms. The CZ operates exclusively on the BNSF through Omaha and always has.
If one were to re-establish use of a legacy station in Omaha, the Burlington Station would make more sense. Assuming, that is, one could convince the TV station to allow use of part of its property as an Amtrak station.
The good news is both stations, Union and Burlington, have been preserved and restored.