After some tinkering, I succeeded to do this. Here is how: first, install the ttn-zh package as described here.
This will have the huge benefit of installing the packet forwarder and configure everything to work with the ic880a. Once you confirm that it works using TTN, use the Raspbian/Ubuntu documentation to install the full stack.
Now comes the magick bit: instead of posting the packets to TTN, configure the packet forwarder from ttn-zh to use the local server:
cd /opt/ttn-gateway/bin
sudo cp local_conf.json local_conf.json-TTN
vi local_conf.json
and change this:
"servers": [ { "server_address": "127.0.0.1", "serv_port_up": 1700, "serv_port_down": 1700, "serv_enabled": true } ],
And finally, configure the rest via the web interface:
https://www.chirpstack.io/guides/first-gateway-device/
And it works! Chirpstack is an awesome software, by the way. Thanks guys!