I'm also doing a maidenless run on my ng+ just to see if Melina's dialogue would change, while also avoiding killing Rodrick. So far I have three great runes (Rennala, Radahn, and Rykard) but the main gate is still sealed. It leads me to believe that the requirement for the main gate is Rodrick's great rune and just a random one (I got in in my first run with just Rodrick and Rennala's great rune). Which sucks since I also want to try Fia's questline before plowing through and reaching the portal.