An illustrative user interface (UI) remote streaming system obtains a UI dataset defining a user-customized UI that provides a client device access to multi-access edge computing (MEC) resources associated with data migration operations to be performed on tagged data resource of a plurality of data resources. Based on the UI dataset, the system streams data to and from the client device to direct the client device to present the user-customized UI to a user. When the system detects that a previously untagged data resource of the plurality of data resources becomes tagged by the user as data is streaming to and from the client device, the system changes a set of UI elements included within the user-customized UI to add an additional UI element for the newly tagged data resource. Corresponding methods and systems are also disclosed.