<p>This paper considers numerically solving constrained pseudo-monotone nonlinear equations arising from various practical application fields, such as machine learning and compressive sensing. It is known that the derivative-free projection method (DFPM) is a classical and effective means of designing numerical methods for the discussed equations. Moreover, the convex combination and inertia are two kinds of effective strategies to further accelerate DFPMs. This paper focuses on designing a family of new accelerated DFPMs for the discussed equations. First, a novel hybrid acceleration scheme is proposed, which possesses two important characteristics. One is that the sequence of acceleration parameters has a very wide selection range including both the classical inertial and convex combination parameters. The other is that the accelerated point is an acceptable approximate solution whenever the algorithm is forced to terminate at such a point. Second, a spectral conjugate search direction is proposed. Third, based on the line search techniques proposed by Amini and Kamandi [Numer. Algorithms 70 (2015) 559-570] and Yin et al. [Numer. Algorithms 88 (2021) 389-418], a modified adaptive line search strategy is introduced. As a result, a family of hybrid acceleration DFPMs for the discussed equations is proposed. Under standard conditions, the global convergence of the proposed family is established. Importantly, we show the iteration complexity in the ergodic sense and the local convergence rate of the proposed family under the locally Lipschitz continuity (LLC). To our knowledge, this is the first convergence-rate result associated with DFPM-based algorithms under such a condition. Finally, the proposed algorithm is applied to solve ten sets of large-scale benchmark instances, the regularized logistic regression and sparse signal restoration. Extensive numerical comparisons with some relevant methods verify the superior numerical performance of the algorithm.</p>