This isn't my area of expertise, but if I'm reading the Michel and Sieger catalogs correctly, here's what y'all have.
Here's the complete schedule for the round-trip flight.

The US covers were transported on the steamers
Albert Ballin,
New York, and
Olympia, and arrived in Friedrichshafen just prior to the flight's departure.
The diamond-shaped cachet was used on covers which began the journey at Lakehurst.

In Germany, a German confirmation stamp was applied.

Upon arrival in Lakehurst on 31 May 1930, a Lakehurst arrival cached was applied.

For covers that were then loaded at Lakehurst, and which only made the final Lakehurst-Seville-Friedrichshafen portion of the trip, a second, slightly-modified cachet was used.

A small number of covers exist with the first cachet used incorrectly instead of the second.
For covers that made the Friedrichshafen-Lakehurst-Friedrichshafen round-trip, an additional violet confirmation stamp was applied.

But again, certain items exist with the confirmation stamp erroneously applied.
So to answer your last point, stampcrow, judging by the addresses, it appears all have the correct markings.
- The initial cover in dis123's post received the initial purple diamond cachet upon mailing, then the red Südamerikafahrt cancel at Friedrichshafen, then an arrival cachet at Lakehurst, where it was offloaded for delivery to Newark.
- LarryBruce's and cfrphoto's covers made the same voyage as dis123's cover, being offloaded at Lakehurst for delivery to NY and Massachusetts, respectively.
- wt1's cover made the whole trip, and has the purple diamond (Lakehurst), red Südamerikafahrt (Friedrichshafen), green Lakehurst arrival (Lakehurst), and purple round-trip.
- My vision's not good enough to tell on bwarren1's covers.
Hope that helps.