Is this likely a narcissus 'Avalanche'? It matches the pictures I've seen online but does not match the picture in the ATP database.

How many flowers per stem? Avalanche should have 15 to 20. You might have Canaliculatus, 4 to 7 flowers per stem. The coronas for Avalanche are described as demitasse-shaped, for Canaliculatus cup-shaped.

I get about four flowers per stem.

Looks like it could be the Chinese Sacred Lily, narcissus tazetta var orientalis chinese sacred lily.

https://www.google.com/webhp?h...

It does that to.
How tall is your's Kelli? Avalanche tops out at 16 to 18 ", Canaliculatus at 4 to 6 ", Chinese Sacred at 12 to 20".

They are done blooming so I can't go out and check for sure but I think the height is around 12 inches or a little more. (Someone on FB said that Chinese sacred lily has an orange trumpet, but I am much more inclined to believe you guys. I had been thinking Chinese sacred lily, too. Whatever they are they are likely something that has been around for a while and it has to be something that naturalizes in warm climates. They came with the house and a neighbor said most of the landscaping was done in 1964 or '65 with little change thereafter, until we moved in.)

The Chinese has a yellow cup, described as 'cheddar cheese'.

Hmm... I always think of "cheddar cheese" as orange.

That's a Brent and Becky description.