Let's follow up this discussion at the Neptune Community
(this forum will be kept in read-only mode)
Running Neptune Apps in the Fiori 2.0 launchpad is not a problem. Actually, Neptune UX Platform is certified for S/4HANA 1610 (ABAP 7.51) which includes the Fiori 2.0 look and feel.
I got some screenshots for you, in this case, running our Time Entry template app.