If you're going to have the York White Roses, then they have to have their traditional rival. I might try the background in black, but green and red is an underrated color combination in my opinion. Let me know if there are any changes that might help these. I did a heraldic rose option for this logo as well, but I think I prefer the top one.
Here it is with a black background: I tried it with red, but I don't think the rose stands out enough for it to work.