Thanks for your input, guys; we did finally manage to locate King Neptune's, but it wasn't easy. On Friday night we circled the whole of Orange Beach in search of the restaurant, and eventually gave up because it was getting later and later and we were starving, and settled for Sea & Suds (? -- Something and Suds, anyway) over the water in Gulf Shores, next to our hotel. The food was average, but they have an all-you-can eat fried mullet special for $5.95 on Tuesdays and Fridays; luckily it was Friday, so at least we were able to sample the mullet. Didn't run into any smoked mullet, unfortunately. Also tried the fried crab claws, which were good.
When we returned to our room we got out the yellow pages and looked up King Neptune's and it turns out it is actually in Gulf Shores, not Orange Beach. It's on the highway that runs from I-10 through Foley and south through Gulf Shores. So we ate lunch there the following day; had the steamed Royal Reds and Dungeness Crab which were very good. I was reluctant to try the crab because it's obviously not caught locally, but the waitress convinced us that they serve so much of it that it's good anyway, and she was right. My mother was also able to enjoy her oysters on the half shell, even though we couldn't come up with an "R" in May, with no ill effects.