Q1: Do you know of any use of this kind of top — possibly historical — that would support the "song top" interpretation?
Well, traditional kyokugoma performances were accompanied by somebody playing music, perhaps also singing.
Miki's 2022 traditional freestyle was with a chonkake, not a kyokugoma, but the idea is the same:
Q2: Have you ever seen a koma of this general design (bowl-shaped rotor on a thin coaxial metal rod) with (a) an adjustable rotor pisition along the rod, or (b) a starting method that doesn't involve throwing or palming the rod? Some string-pull gizmo perhaps?
(a)Yes, the rod can slide on some of these komas to adjust the tip to stem ratio (as well as in regular komas). In particular, the budget kyukugoma that Spingear offers is like this.
(b)The other traditional kyokugoma starting method is the swing technique between the thumb and the index fingers, specially for the larger ones (furikoma = swing top).
I don't recall seeing them started in other ways, but I bet it has happened.