mac pro airdrop - no other device can see the Mac.

I cannot for the life of me get Airdrop to work on my 2013 trashcan Mac Pro. I can Airdrop files to my iPad or my laptop, but the other direction does not work - the Mac Pro does not appear as a device in the AirDrop pane.

So far I have:

• toggled wifi and bluetooth on both devices
• ensured that I am on the same wifi network on both devices
• restarted both devices
• ensured that my firewall is turned off
• ensured that I am logged in to iCloud using the same account on all devices
• logged out of, and then back in to, my iCloud account on both devices
• set Airdrop discovery options to "everyone" on both devices
• reset my P-RAM
• ensured that "Do Not Disturb" is turned off on both devices
• deleted all of the bluetooth preferences files in /Library/Preferences
• rebooted again
• disabled, and then re-enabled, Airdrop from the command line
• rebooted yet again

All of my devices are within three feet of each other, and in fact I can actually tether my iPad to my Mac Pro using Bluetooth, so range can't be the issue.

I am running macOS 10.14.4 Mojave on the Mac, and iOS 13 on the iPad. I also have a MacBook Pro, and Airdrop on that machine works fine. Both the Mac Pro and the iPad can see the MacBook. The MacBook can see the iPad. Nothing can see the Mac Pro.

I'm kind of at my wits' end at this point. Does anyone else have any other suggestions?