I guess you can say there isn't one, but the Pearl, Legend and any of the Yamahas, many of them signature snares, of that same era.
I think the shell hass less influence when you go to those sizes especially if you use wires wth lots of strands. It's all attack and snares. My Colaiuta sig sort of does that job for me. Though I don't know about any issues personally, those single screw lugs on the Yamahas are considered a weak point.
The only piccolo I'm really interested in myself is this one.
That ^^ snare sounds so good I want to cry.
Piccolos are , it seems snare drum that most drummers at least try. I tend to only like piccolos that sound good tuned medium-medium low (not cranked up high) . These are the ones that I have crossed paths with :
I used to own one of those wacky 13x3" Ludwig piccolos with the offset double sided lugs. Didn't care for that very much. Fast and small sounding.
I used to own a Craviotto Birds' Eye Maple 4x14 that was really great, wish I still had it.
I used to own a Stanton Moore Spirit of New Orleans 4x14 titanium. Yawn. Sold it quickly.
I used to own a Pearl 3.5x14 Free Floater maple shell. It was very nice. Not really versatile IIRC< I think it only liked to be tuned high.
I used to own a Dixon 3.5 x14. Mediocre at best. Fell apart. Threw away.
I used to own a Yamaha 3.5x14 brass Nouveau - had a hard time with this one...tuning issues, again drum seemed to only like high tuning
Currently own two Yamaha Maple Custom Absolute piccolos - a Blue Sparkle 4x13 and a Green Sparkle 4x14.
Wish I could find a Garabaldi or one of the brass Yamaha piccolos others have mentioned ^^^