Duh. I’m such an idiot. I should not be allowed be called an engineer at all. So In my haste to find the cheapest relay I forgot that I needed one with all 5 pins. See, a relay works by using a magnet to pull a switch. The magnet is powered by 2 of the pins, the input to the switch by one pin and the switch points are the other 2 pins. The relays I bought only have a pin for the ‘on’ contact of the switch.
To make an XOR gate and an inverter my design calls for relays that have connections of the ‘off’ contact of the switch as well. Luckily most of the gates in our design are not XORs or inverters so all is not totally lost but I will still need to use 2 different kinds of relays which will not look cool at all. I’m going to have to try to find 5 pin relays that look and act exactly the same.