Marinate on this. When a new case arrives that looks like it will incur significant fees, have a capable firm (the budget firm) prepare a budget — with its key assumptions expressed clearly. Tell the budget firm that another firm will have the opportunity to represent the company in the matter for whatever amount is the budget the first firm proposes.
Then, have a second capable firm (the review firm) review the same facts you gave the budget firm as well as that firm’s budget and assumptions. The review firm can agree to handle the case for that amount or pass. Neither firm knows the name of the other firm and the roles should be swapped randomly (and perhaps a third capable firm thrown into the mix from time to time).
This all may be too clever by half, and certainly no two firms are wholly fungible, but consider the logic: it is much like one child breaking the cookie in half and the other child getting to choose which half to eat. The budget firm will try to be realistic, because a fat budget will be snapped up by the review firm. And if the review firm declines, the law department has a market-based measure of the leanness of the proposed budget.