We consider LieG-valued Yang-Mills fields on the space ℝ × G/H, where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifold ℝ ×G/H carries a G₂-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on ℝ ×G/H is reduced to Newtonian mechanics of a particle moving in ℝ⁶, ℝ⁴ or ℝ² under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)×U(1), Sp(2)/Sp(1)×U(1) or G₂/SU(3), respectively. We analyze all critical points and present analytical and numerical kink-and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S¹ ×G/H and dyons on iℝ ×G/H are also given.