The model could choose which measurement operations to make on the qubits, and which operations to take to repair the qubits?

In some quantum error correcting codes, there is a large set of operators that, when there are currently no errors, measuring these will not change the state (well, assuming the measurement is made without error), but would result in some information about the kind of error if there is an error, and this info can be used to choose what operations to take to correct the error.

For a number of such schemes, there’s a choice of a strategy of what schedule to check which of the measurements with, and how to correct the errors.

The way you describe this reminds me of the quantum bomb tester (Elitzur & Vaidman). Uhhh so this is treating a potential environmental interaction the same way as E&V's "bomb"? With at least the new wrinkle that there are multiple potential bombs, each with low probability?