>> I'm still at a loss as to how you self-arrest (effectively) with a spike-ended tube.
>>>> are you talking about op's desire for a shaft with a grip and no axe head? i don't think the plan is to self-arrest, just self-belay.
>>>> If you're talking about the petzl snowtube, as pointed out, it’s just a variation of a picket for anchoring a belay, not (meant to be) a substitute for an ice axe.
As the OP, I can say you are mostly correct. I mainly want this for self belay. But in a pinch, on soft snow, you can use a spike ended tube for self arrest. I would grab it a few inches from the pointy end with my left hand (I'm right handed) and somewhere towards the top with my right hand. (I would figure out the strength of the tube before leaving the house). You wouldn't have the hammer motion you have with an axe, so you wouldn't be able to penetrate hard ice, but on snow it would work better than your fist* or even a regular pole (since a pole won't go down as deep). The key is to match your technique with surroundings. On hard snow or icy snow, I would self belay the entire way. On softer snow, with a better runout and a more moderate angle, I would use it as a half-ass arrest tool.
* Knowing how to self arrest with your fist is important, in my opinion. You could always lose your ice axe, or encounter unexpected snow on a loop trip. Again, I wouldn't depend on it if failure meant death, but I've used the technique to avoid nasty scrapes.