I have a problem similar one described here: Access Document ID from a different Site Collection

I have one site collection (on webapplication1) and record center, as separate site collection on webapplication2. On both of those site collections I have Document ID service enabled and configured. When the time comes, i want to move document from first site collection (and leave a link) to the RC. On first site Document ID still works, (says that document was moved, and points to Drop-Off library) but when document leaves the drop-off library, it can't find the document anymore.

Moreover - on the Record Center, the old Document ID is still assigned, but clicking on results in 'Document with following ID was not found' error.

I was trying to rerun following timer jobs - Document ID assignment job and Document ID enable/disable job on both web applications, but it didn't help/change anything.

Am I missing something, or it's just this Document ID feature is lacking something?