Did not have the overlay on to see it and I would need to wait another couple of hours in a queue to retestBut yes the main thing that would be impacting the latency is lack of reflex, low FPS and not having dedicated/premium servers. What was the latency being recorded with free tier on your system?
I did mess about with LAN streaming and to be honest 1440p 120Hz did feel pretty good. I tried 2160p but the old 3080 probs can't encode 4K 120Hz so cap was about 60fps - it did not feel good!
As long as you live close enough to a datacentre and can stream 120fps it is probably not bad actually!
Some Moonlight stats: