"I'm actually French and I was looking for the exact way Americans spell this word… And I still don't know after reading all this. But I can tell you how to pronounce it:

it's not Ray-Zoom-May
it's more like Ray-zuum-may"

Benoit - I've noticed that Americans don't really make that sound in their speech. Witness "puma" and "dune" which they tend to pronounce "pooma" and "doone" rather than "pewma" and "dew-ne."

full disclosure: English trap/bath split adherent living in US for 10 years.