Plane wave basis sets offer many advantages in ab initio molecular dynamics due to their efficiency and simplicity. In combination with hybrid density functionals, they become computationally expensive due to the evaluation of the Hartree-Fock exchange energy. The computational cost can be significantly reduced by screening the Kohn-Sham orbital products after localizing the orbitals in real space. However, such a procedure introduces apparent errors in the wavefunctions and nuclear forces resulting in unstable dynamics. It is shown here that a noise-stabilized dynamics approach can overcome this problem and at the same time permits using insufficiently converged wavefunctions for evaluating atomic forces. In this way, we achieve significant speed up even for a small system containing about 100 atoms. After benchmarking the accuracy and efficiency of this approach, we use it in combination with well-sliced metadynamics to compute the free energy barrier of formamide hydrolysis in alkaline aqueous medium. These results provide insight into the error of the Perdew-Burke-Ernzerhof functional in predicting the free energy barrier for hydrolysis reactions in water.