Mechanics only get a set amount per repair from Ford for warranty work and I’m not sure about non-warranty. So, if they think the repair is paid at 4 hours work, and the mechanic can reasonably do it in 4 hours with no interference, etc it’s an easy gig. OTOH if it’s billed at 4 hours and it’s more like a 6 hour job, they’re less motivated to do the work.
Here, I’m not understanding why there’s a delay. There’s nothing modified with the front diff or even remotely related to it. You should be calling Ford C/S every day for updates. Dealer too.
There’s no excuse to not cover the repair given the circumstances you’ve explained.