My point is can you connect that second 1080p monitor to the streaming PC and display that information from that computer? What is it that you're displaying that needs to be on your gaming rig?

So, lets talk about your network, you are using wired connections for all of this right? If so, TP-Link has a 5 port 2.5GB switch for ~$130 USD - https://www.amazon.com/TP-Link-TL-SG105-M2-Multi-Gigabit-Wall-Mount-Protection/dp/B08ZHGT2ZP/ref=sr_1_3?dchild=1&keywords=5+port+multigig+switch&qid=1628711296&sr=8-3 - that will provide more than enough speed between the gaming computer and the streaming rig for NDI. You can pickup 1x PCIe network adapters for ~$40 USD.

Also, if you don't mind sharing, what capture device are you using that supports 1440p120?