We define P-strict labelings for a finite poset P as a generalization of semistandard Young tableaux and show that promotion on these objects is in equivariant bijection with a toggle action on B-bounded Q-partitions of an associated poset Q. In many nice cases, this toggle action is conjugate to rowmotion. We apply this result to flagged tableaux, Gelfand-Tsetlin patterns, and symplectic tableaux, obtaining new cyclic sieving and homomesy conjectures. We then study cases in which P is a finite, graded poset other than a chain, yielding new results for products of chains and new perspectives on known conjectures. Additionally, we give resonance results for promotion on P-strict labelings and rowmotion on Q-partitions and demonstrate that P-strict promotion can be equivalently defined using Bender-Knuth and jeu-de-taquin perspectives. Finally, we explore conjectures, related and unrelated to our main theorems, on objects that promise beautiful dynamical properties.