So given that context, it doesn't sound to tough to add a cost to the type for each operation, function call, whatever, and have the type checker count up the cost of each call. So you'd have real proof that you're under some threshold. I wouldn't put the agda runtime on a flight control computer. But I think I could write a compiler, now, For like a microcontroller that would count up (or spend time budget, doesn't matter).
A more sophisticated computer would be way way harder, and be resource efficient. But if you modeled it as "everything's a cache miss" and don't mind a bunch of no-ops all the time, that would be a pretty straightforward adaptation of the microcontroller approach.