I am doing the same experiment. I have 6 pay relays, almost the same as you. Because of how some clients work, you need to have your updated list on some popular relay, so I have one in write mode only.

My experience is the same as yours.

The workaround I see is to enable some popular free relays and use a client that lets you choose what relays to see in Global, for now I only see Nostros doing this. But I think this would be very welcomed in other clients.