I've fished Stone off and on for years and have never been there when the spit breaches. I know it does breach but it's always closed when I've been there.
A float tube is great for getting around although if you want to really explore different parts of the lagoon, you might consider something with more mobility. I like the north end parking lot because there's a nice cove in that area that you can work. I've heard you can catch fish along the spit but I've not had much luck there.
Agree on the recommendation to check in at the Eureka Fly Shop. The owner (Mike) was featured in Bill Sutherland's book Fly Fishing California Stillwaters, specifically in a chapter on Stone Lagoon.
Wild Bill
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