Pissing off HR never ends well. Ever. Bear that in mind when you send your challenge.
Were it me, I'd email your hiring manager and/or recruiter in addition to the HR department but just let them know that you have a job offer and that you have to give them an answer by a certain date. Actually "challenging" them probably won't end in your favor.
Don't ask them to move forward without a reference check. It can serve no positive purpose. Either they can or they can't. In most cases, they can't. Believe me, they know that you want them to do so. But policies such as these are usually immutable, especially if the company is large.
When I got contracted to a Fortune 15 company, they needed a 10 year background check. It took a month and toward the end they were preparing me to accept that I wouldn't get to start. Everyone apologized, but you're not going to make an HR department ignore what they're told to do.
Unfortunately, you're just one person and in the eyes of an HR department, you can be replaced easily. The only person who has even a prayer of getting a policy bypassed would be someone inside the company. Even then, it's unlikely.