The issue is resolved for me - when placing the edges on NSX-prepared hosts, the geneve tunnel traffic has to be placed on a separate NSX-segment. So, if someone has the same issue, create a new VLAN NSX Segment, add it to a VLAN TZ, add the TZ to your edges. This way you will be able to select this segment for your tunnel traffic.

The NSX design reference guide has just recently been updated to match NSX 3.0 (no 3.1 still...), I hope the business unit steps up in this regard.

edit: I have no idea how to mark the post as "resolved" after the recent vmtn update, so I'll just mark my answer as the correct one.