This is just my personal opinion and other posters have had different experiences, but I find moissanite warmer than F-H stones. I prefer to wear it on it's own or next to a plain band or paired with my LY Winfields brand solitaire because I find the colors more compatible. Personally, I like the colors of my white stones to match between e-ring and wedding band.
Now I like warm stones a lot and love moissanite in the smaller sized stones - what little fireballs they are so am not against moissanite by any means. I just wanted to point out I find it runs warmer than the Asha colors and you might also find the difference bothersome. I specifically sold a ring because the moissy accents on it clashed with the F/G diamonds in the wedding band I wanted to wear it with.
So I would give Moissanite Co a chance for sure. But, you might want to stick with diamonds of the same color as your Asha for a perfect color match. But that wouldn't be bad - then you can go buy some moissanite earrings or pendant and increase your jewelry wardrobe! You WON'T be sorry!