“We don't have the bandwidth to evaluate this.”
Why they say it. Evaluation feels like work added on top of an already full plate, and the payoff is uncertain. It is a real capacity constraint and a convenient deflection at the same time.
Do not: Do not pile on a heavy trial or a long form to fill out, which proves their point that you will cost them time.
That is exactly the kind of thing I do not want to add to, you are clearly underwater already. So let me carry the load, I will do the legwork, tailor it to your situation, and keep your time to the few decisions only you can make. If I made evaluating this cost you under an hour total, would that be worth it to see if it buys your team time back?
Then ask. If the reason you are too busy is the exact problem this solves, when does that loop ever break on its own?