Solved! but it's a hassle...
After talking with Apple Support, we determined it's probably due to a faulty version of iOS on our phones. I restored my phone in recovery mode and then restored from a backup. AirPods+ iPhone have been working perfectly since then (24 hours!) with no audio stops or phone call audio issues.
Here are the steps I followed:
Backup
1. Backup your phone to iCloud and turn off find my iPhone.
2. Backup your phone to your computer using iTunes. (It'll restore faster from an iTunes backup plus horcruxing your phone is always a good idea.)
Restore
3. With your phone plugged into your computer and iTunes open, put the phone in recovery mode. On my iPhone 7, you hold down the sleep/wake button and the volume down button simultaneously until a "connect to iTunes" logo appears.
(enter recovery mode instructions for different iPhones: If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support)
4. iTunes will tell you "There is a problem with the iPhone that requires it to be updated or restored." Follow the prompts to restore (not update) the iPhone. This step fully removes the faulty version of iOS on the phone and replaces it with a new copy that iTunes will download.
Setup from backup
5. After the restore is complete, set up your phone from one of the backups you made in steps 1 and 2. This step puts all your information and data back on the phone.
6. Once you've finished setting up your iPhone from the backup, try using AirPods. Hopefully the issue is resolved.
It's been 24 hours since I did this process and I have not had any problems with my AirPods since then. They're working just as well as they did before the iOS 11.3 update when this started happening all the time. It was to the point where audio would drop on nearly every track or podcast I played. Now they work normally again. It was a time consuming fix, but well worth it to get this unbearably annoying problem resolved. Hopefully it works for you guys too!
Shout out to Steve at Apple Support for the idea
