I used to be a registered investment advisor and used fidelity as a custodian.

 The person sending your IRA has no incentive to do so quickly.... The longer they drag it out, the longer they continue to collect their percentage of AUM. 

 It's always quickest, to liquidate your holdings and transfer cash. Proprietary assets can't be transferred "in kind" , and if you tried to do that, the back office could halt the entire transfer.... because... incentives 😉

Fidelity usually doesn't f up the receiving of assets. However, they have weird account numbering which needs to be handled with care when submitting transfer paperwork.

If the receiving Fidelity account  has a letter prefix, you need to modify the account number (i.e., swap the letter for specific numbers.) when you fill out the transfer paperwork. Otherwise, fidelity won't recognize the account and either reject it, or keep it in a "bucket" account until someone figures out where it goes.

Happy to review the paperwork and help troubleshoot. It should be a quick fix.
🙏