At the moment it seems to be fixed by a workaround.
"mac adr off" - this was on
"mac ar off" - this was on
"max tx uncnf" - rather than "mac tx cnf"
This feels wrong, but at least the packets are forwarded to TTN now. Likely it will be received by the proprietary network too, but this is not currently a problem (security wise it might be in the future).
My best explanation for these settings solving the issue is that the proprietary network gateway configured my node to use a different channel/data rate through ADR. Maybe one that can not be received by the TTN gateway.