  In this letter, starting from a kinematic Hopf algebra, we first construct a
closed-form formula for all Bern-Carrasco-Johansson (BCJ) numerators in
Yang-Mills (YM) theory with infinite orders of $\alpha'$ corrections, known as
$\rm DF^2+YM$ theory, when coupled to two heavy particles which can be removed
through a simple factorization limit. The full $\alpha'$ dependence appears
simply in massive physical propagator factors, with factorization strongly
constraining the construction. The intricate structure induced by the massive
poles also naturally leads us to find a novel closed-form and local expression
for BCJ numerators in usual pure YM theory, based directly on the kinematic
Hopf algebra.
