I suggest discussing this with the powers to be, QA, and any committee involved in transfusions, budgets, unnecessary, wrong collections etc. Present your concerns and suggestions and if you are overruled you have evidence of your due diligence.
While I see arguments for both sides; finding the most efficient and safe process that everyone can agree with is the important concern. If this means extra draws, cost and BB time so be it.
Biggest risk maybe drawing two tubes at the same time (one draw) and writing different times (two separate draws)!!