I no longer think that this bug is caused by kaslr. I have actually narrowed down this problem to the bootable USB disk that I am using to boot the operating system. I should have mentioned in my initial message that I am booting the system from a USB disk using a read-only partition.
The problematic USB device is a SanDisk Cruzer Fit 8 GB USB 2.0 Low-profile Flash Drive (SDCZ33-008G-B35). I have many of these, and have tried over a dozen of them. They all cause the "Initramfs unpacking failed" error on about 10-15% of bootups. Annoyingly, I've counted over 100 bootups (with physically different matching PCs) and marked which ones fail. The failures occur seemingly randomly about 10-15% of the time.
Previously, I used several of these USB flash drives (which don't exhibit the problem at all): SanDisk Cruzer Fit CZ33 16GB USB 2.0 Low-Profile Flash Drive (SDCZ33-016G-B35). These boot perfectly 100% of the time on the exact same PC hardware.
Furthermore, I am using the same bootable image on both types of USB devices; I use a script to create identical-sized partitions, copy necessary files to the partition using fsarchiver, and then I have USB flash drives with identical images. I should note that the primary boot partition is only 3.5 GB, so all data fits on either SanDisk device. The SDCZ33-008G-B35 exhibits the problem described in this bug report; whereas, the SDCZ33-016G-B35 does not. The same data is on both devices, and they are both running on the exact same hardware. I've tried different PCs (identical PCs, mind you), and the problem is consistent.
The processors are not overclocked. The BIOS performs a RAM test at boot (I haven't tried memtest86+), but I don't think RAM is a problem here. Like a mentioned above, the problem does not occur for the other 16 GB USB flash drive on the same hardware.