District crossings are tricky, but I worked out that the export slider works based on the amount of available/spare storage for the resource in question, in the target district.

Unfortunately, the gargantuan pile storage DOES NOT WORK with district crossings. The storage offered by the gargantuan storage does not count towards the district crossing's calculations, and therefore the district crossing *will not export* goods destined for gargantuan storage.

Example: I had a gargantuan scrap metal in district 1, with 3k spare storage. District crossing set to export from District 2 did not "see" the 3k spare storage, and only counted underground piles etc... therefore the district crossing thought no spare storage was available in District 1, and therefore no export.

Workaround: Set a vanilla storage up for the resource - probably near the district crossing - and set it to "Supply" and "Prioritise by haulers", and have your gargantuan storage set to either "Accept" or "Obtain". This way the vanilla storage should always have space and the district crossing should see the spare space and therefore create a demand for the resource.