So Lovely fits your description. Diploid I use it in hybridizing.

Joan Senior is the most white of all of mine and more white than many, but a bit short. Has seed pods all the time from bee pollen so very fertile. diploid

Brad

Boundless Beauty seems to be a good one. 2nd year for it in my garden and produced 17 to 23 buds per scape.

I like my Heavenly Angel Ice.

I like White Tie Affair. It's not a tall day lily, so it needs a spot on the front row, but its flowers are large and not down in its own foliage. Mine come back up every year, so they should return fine for you, too. I've had one for several years and two more for a couple years because one wasn't enough. I get lots of beautiful flowers from them ... until the deer come along and eat all my day lily buds.

I forgot to mention TET, which is important. My fault. Brad otherwise nice though I would prefer a bit more ruffled and rounder. Nancy 'Boundless Beauty' might be good and seems to check most/all the boxes I indicated. I see some photos that are excellent, others where the flower is not real flat, though it is a BIG flower, good color etc. Do you have a photo of it in your garden?? Any more suggestions.?

Here are some of our best whites. I can't speak to their fertility since I don't breed for white.

Our best white is See Me-Feel Me-Touch Me. It's a great grower for us.

Lime Frost is a late bloomer and tends to be whiter than some.

Winter Treasure is a rather short plant. We don't grow it anymore, but my recollection is that the flowers are above the foliage.

Buzz Saw is another we grow. It tends toward yellow.

I don't have a good picture of it and we don't grow it anymore, but Blizzard Bay is another near white.

Nancy

I forgot Last Snowflake.