Predictions of the mass of the lightest charmonium hybrid meson, using the "flux tube model", are in the range 4.1 -- 4.2 GeV.
http://arxiv.org/abs/hep-ph/9501405
Nucl.Phys.B347:854-868,1990
Phys.Lett.B129:351,1983
More recents calculations, using "anisotropic lattice", predict a
somewhat larger mass, 4.3 -- 4.4 GeV
http://arxiv.org/abs/hep-lat/0206012
http://arxiv.org/abs/hep-lat/0210030
As for the decay, the main difference with ordinary mesons is that the decay to open charm would be suppressed, except for daughters having different parity.
http://arxiv.org/abs/hep-ph/9411301
The actual threshold would therefore be Ds(1968)+Ds**(2317)=4285 MeV ..
