Have you checked the following topics already?:
The hard RAK831 cafe part 3,
The hard RAK831 cafe part 2
The hard RAK831 cafe part 1
As has been said before above, you can just use Raspbian for a LoRaWAN gateway. It is not required to use RAK Wireless’s OS image for RAK831.
You should be able to run the gateway software in addition to the MQTT broker (‘plus a couple of other things’) on your existing Raspberry Pi - assuming that the MQTT broker and ‘other things’ do not put a heavy load on your RPi.
How to install TTN Gateway software on Raspberry Pi without custom pre-configured OS image:
There are several gateway (packet forwarder) implementations and installation procedures available for Raspberry Pi.
For installing the gateway software onto an existing Raspberry Pi setup (without the need to first install some custom pre-configured OS image) I like the setup procedure described here: GitHub - ch2i/LoraGW-Setup: SX1301 Lora Concentrator Raspberry PI based gateway setup
This setup procedure supports multiple SX1301 concentrator boards RAK831 included and uses the multi-protocol packet forwarder (by @kersing) which is more secure than the basic packet forwarder used in some other setups (e.g. GitHub - ttn-zh/ic880a-gateway: Reference setup for iC880a gateways running The Things Network).