Maybe it arrives too late at the gateway, due to large network latency. What handler are the applications registered to? What do the gateway logs tell you? All your gateway traffic shows SF12; can you try to use a better data rate? (SF10 or lower increases the chances that TTN will use RX1 rather than RX2. Of course, both RX1 and RX2 should work.)
The sole facts that the ABP device’s downlink does not work, and that the OTAA join does not work, do not prove that the problem is related to sending the downlink to the gateway. Maybe the downlink arrives at the gateway perfectly in time, but the gateway does not support the settings that TTN wants, like see ERROR: Packet REJECTED, unsupported RF power for TX - 24. Or maybe the gateway is actually transmitting it just fine, and the node’s timing is not sufficient accurate. You cannot tell unless you can peek in the logs of the gateway or do some actual measurements using an RTL-SDR dongle.
Then I’d very much recommend an RTL-SDR dongle anyway.