The existence of the $SU(2)_L$ triplet composite spin-1 resonances $ρ^{±,0}$ is a universal prediction of the strongly interacting new physics addressing the naturalness problem. Such resonances have not been found in the diboson final states, which are expected to be the dominant decay channels. In this work we propose a new scenario where the left-handed quark doublet $q_L=(t_L,b_L)$ is fully composite. In this case, the ρ resonances can be broad and mainly decay to the third-generation quarks. The $t\overline{t}$ resonance search channel is comparable in sensitivity to the dilepton channel. In addition, the same-sign dilepton channel in $t\overline{t}⁢ρ^{0}$-associated production can probe the large-width region and complement the Drell-Yan production channels.