In a way I'm reluctant to share this, and dont want to disillusion anyone following social protocol, but Cash talks... similar has happened to me twice. Both times, just passing through and wanted immediate service if possible, but striking out with every call (best I could manage both times was 4 days wait time). With a last resort effort, I explained my situation & desperation to the Service manager and kindly offered $200 if he could get me to the "front of the line". Both times worked, and i only incurred a one day layover. Both instances were not minor repairs, but your situation seems to call for considerably more.
Disclaimer: I did have reservations making the offer (Not normally that kind of personality) but circumstances nagged me to try