Some year ago I sowed a whole packet of Hakone White(double). I do not recall a single plant with 'blindingly white' flowers. Best case scenario was 'off-white'. The rest was more or less very light washed out violet, either the whole flower or the rims. Some had irregular stripes of colour.

There is a cultivar called 'Axminster Streaked' that has splashes/flecks of blue-purple on white. Sometimes you see them with pretty large splashes of color too. Yours does sound very neat ;-)
CMK

This was from a packet of seeds sown about 10 years ago. They were supposed to be white and only 10-12 inches tall. Unfortunately I don't remember the variety, though I guess it doesn't matter as they were obviously not what the packet said. I did get some lovely whites but all were at least 2ft.

Here is a link that might be useful: balloon flower

hostaholic2 - wow! love that striped balloone flower! Have you ever grown any from seed? does it come true? It's gorgeous!

I have had some seedlings from it but they have been either white or blue.

hostaholic2- the mottled flowers looked fairly similar to that, though they were primarily purple mottled with white.

Still trying to find the photo of the half and half flower. That one was very unique.

Hope you can find it.