Just wanted to provide an update on this.
In the support ticket we have traced the problem to an invalid value of the <BirthDate> property within the userConfig.xml file, within the <Contact> section. The issue is that I had set my birthdate sometime prior to V16 and the value was saved as MM/DD/YYYY. When I compared that with another account which did not have a birthdate set prior to V16, saving a new value in V16 goes in as DD/MM/YYYY. So the month date date were reversed.
It's quite possible that this is a bug affecting *any* user that had set their birthdate prior to a V16 upgrade, where the month / day are reversed in the userConfig.xml file. However, that would only cause an error if the user's day of the month for their birthdate is 13-31 (mine is in that range). In addition, we are located in Canada although our servers are set to en-US - so some strange locale issues may be happening as well. In any case, now that we've identified the root cause SmarterTools can figure out the extent of the problem and implement a fix.
So the reason this mattered is that there's a call to /api/v1/settings/user-mail which is used on the Calendar view as well as on the Settings pages (and others) which wasn't handling an invalid date exception and returning a Bad Request response. Because of that response the rendering / javascript processing of affected pages would break. Again, I think there's going to be lessons learned from this that will make SM16 better for everyone - so that's great.
I'm still back to the original request that's part of this thread though. The z-index of the main navigation bar at the top of the page need to be higher than the loading modal because if there is a rendering / javascript / angular issue that causes the loading modal to stay activated there's no way for the user to navigate to a different page other than using the browser's back button.
Thanks to Derek & Robert for their support on this including providing a custom build to help with the diagnostics.