I'm only familiar with ocarinas, but if both ends are closed and you only have finger holes in it, then it's a Helmholtz resonator and thus a vessel flute. Vessel flutes typically have a neck (it's the air motion in the neck that produces the resonance as it acts like a mass on a spring), though I don't think they need to have one, if the instrument itself is already a pipe.

There are examples of flute like "ocarinas", like the instruments of MountainsOcarina



Or the gemshorn:



But the most telling thing is the sound. All ocarinas of the same volume basically sound the same. A tenor gemshorn sounds just like a tenor sweet potato ocarina, simply because vessel flutes produce only one note. Once you know the sound well, you can usually tell if you're listening to an ocarina or not.

Project Update: I'm backtracking and trying at this point just to make a basic wooden inline ocarina. Plainly I'm never going to get anywhere with the branched design until I can make a decent wooden fipple.

Project Update: Had some success with the basic ocarina project, though I start to lose sound or volume when hitting the high notes (when all four holes are uncovered). Could use better tuning and I think I could still do better on the mouthpiece, though. In the meantime, real life--and to some degree project burnout--is slowing me down. At least now I know that I should make sure the mouthpiece works before I start carving out a big y-cavity.

I don't know much about ocarinas, and maybe Ocarinaforest could say better: but wouldn't it be possible to carve your wye chamber and attach, say, an appropriately sized recorder mouthpiece to it? I'd think this would solve the problem of reinventing the wheel and then allow you to progress towards solving the problem of the wye shaped flute.

_________________
-- A tin whistle a day keeps the racketts at bay.

-- WhOAD Survivor No. 11373

It might be, whistlecollector, and thank you for the suggestion, but as I'm a stickler for detail and want the end result to look as close to the original as possible, so I'll have to solve the problem eventually.

I don't know why I'm having so much trouble with making a simple mouthpiece. Because really, hollowing out one or two chambers from a piece of pine for a test is the work of a few happy hours with a gouge. It's the rest I'm having problems with.