When using LoRaWAN, inverted IQ is not going to be your biggest problem.
True mesh networks between LoRaWAN nodes are not possible, not so much due to technical limitations but above all due to the LoRaWAN protocol: Class A nodes are simply only listening after they transmitted themselves, and if a Class C node is listening all the time then that’s just on a single frequency. See also https://www.thethingsnetwork.org/forum/t/relaying-iot-messages-using-mesh-networks/4614.
Using a repeater/relay gateway will not get you a compliant LoRaWAN network either, as timing for downlinks is very critical; once a true gateway is sending a downlink in RX2, there is no way for some repeater to re-transmit that in time for an actual Class A node, which is only listening at specific intervals. That includes downlinks for OTAA Join Accepts. See Lorawan repeater and https://www.thethingsnetwork.org/forum/t/repeater-behaviour/4743.
Note that in the latter, a post explains a bit about bare LoRa (rather than LoRaWAN), which are not to be confused:
Of course, The Things Network is about LoRaWAN.