There was a process in the past whereby the requests were reviewed by a committee of parliamentarians. I think it was chaired by the Speaker's office, and you had representatives of all parties, and then it went forward to Treasury Board. It wasn't fully independent, but it certainly provided greater oversight.
There's the example of the Parliamentary Budget Officer, or Elections Canada. The idea is to have less approval by the Treasury Board and the executive and more approval by the speakers or the Houses. There are tools, and I think the key point is more legislative involvement.