One problem I see is in determining the amount of time before resuming. You have to be sure that all possible inputs will take less time than what you request, but you don’t want to wait forever. You also have to be robust against disturbances due to things like system load. If you specify a maximum time based on the no-load scenario, then an attacker discovers that they can bog down your system by flooding it with packets while it does the computation, you’re back to leaking info.
Yeah, a dispatcher would have to be designed to guard its secrets. For example, it'd have to ensure that it can do tasks in whatever window it needs to, have a logic for simulating CPU-load if an attacker might be able to watch the CPU's process load, potentially force the CPU to burn more power if we're trying to protect against power-analysis, etc..
Logically, it'd seem like a more complex task since we'd have to keep track of what secrets we're guarding and planning an execution strategy to meet those criteria. But, it feels cleaner to acknowledge these criteria and ensure that they're being addressed.