BINGO - I have a match. The bobbin in the New Home is the same measurements as you gave. However the case does not have the latch like yours does. It's significantly larger then the SH bobbin. The FW bobbin does fit, however it's not as tall so I don't know if that would cause problems, but you could put a washer behind it if needed. The best fit is the White - it's a hair wider in diameter, but it does fit in the case. It is closer in height.
It all depends on if the latch will close using one of these two.
I don't know much about bobbin washers, other than the folks on the long arm board I visit often use them to get a better fit for the bobbins when they buy pre-wound ones.
First time I heard "bobbin washer" I was thinking "golf ball washer" and wondering just why they needed to wash their bobbins . . .