This work generalizes the one-channel Covariant Spectator Theory (CST) formalism to describe quark-antiquark mesons of arbitrary spin-parity JP. We also improve the quark-antiquark interaction kernel by incorporating the momentum dependence of the strong coupling. Within this framework, we perform global fits to the masses of experimentally established heavy and heavy-light mesons with JP=0±,1±,2±,
Nearby in the stack
and
3±
. With only eight adjustable parameters, the model yields an excellent global description of the observed quark-antiquark spectrum and predicts both unmeasured states and likely
JP
assignments for states with unconfirmed quantum numbers. In particular, our results support the identifications of the recently observed
Bc(1P)+
candidates as
0+
,
1+
, and
2+
states, and the
Bc∗+
as the lowest
1−
state in the bottom-charm sector, as well as the
Ds1(2933)+
as axial-vector state in the charm-strange sector.