Get a tug to pull you out a bit.
According to a knowledgeable CFM gentleman, up to 15 minutes warmup is still beneficial to the longevity of the engine, which translates well into direct fuel savings due to low(er) burn for long(er) time.
Though I understand you speak of IAE engines, which at least on the small bus really have a lot of ground idle thrust, pitty you cannot make it out on just one.
Towards the core of your question, I have nothing to add. It is an odd situation hence you came here with it. The suggestion with a tug is serious - beancounter's business as you have already pointed out.