So after trolling several other forums, I came across a solution for this issue that required the creation of a bootable USB thumb drive with a 64-bit boot image. The person posting said that the "default" boot image was 32-bit since multiple boot images were being offered to the "all unknown computers" collection. We have task sequences deployed to this collection for all operating systems from XP to 8.1 in both x86 and x64 flavors. You would think that a system with a 64-bit architecture and UEFI would automatically boot the 64-bit boot image, but I guess that's not the behavior of SCCM 2012 R2.
If anyone else can figure out how to automatically have computers boot the appropriate architecture when multiple boot media are offered, I'd love to hear about it. Until then, I'll either disable UEFI and go with the old BIOS, or have a few thumb drives ready to go...