Hey Cameron, I have two options you can try (try both):
'''Option 1'''
Try to [https://www.playstation.com/en-us/support/system-updates/ps3/|download the update from Sony's website] and put it on a flash drive and install via USB.
'''Option 2'''
As the update will start pull out the HDD (litte plastic cover on bottom of the PS3 and one screw). Then it should run to 99% and stop without any messages. Then, unplug the power to restart the system. At the next restart it will run to about 45% and then jump to 100%.
-Let me know how it goes.
-Please accept this as the answer if it answers your question.