Those are the problems that every govt funded project faces, but they are particularly tough in software. We have many examples where it went very wrong so not many governments acting in good faith are eager to step into it. And you can't allow the government to intervene in development or management here, because this how you'll end up with government-mandated preinstalled browser on smart phones or with added backdoors.
One solution could be participatory budgeting where the end users will directly decide where to invest part of their govt-collected taxes. E.g., on your declaration you'd have a field where you'd like to invest X% of your paid taxes into project Y. This comes with its own set of challenges and admin overhead, but I don't see any other good solution for cases like this, because they are impossible to run under direct government control.