So upon a quick comparison between the two config.sys files' USB sections, I saw that the installation with the working mouse/keyboard has two back-to-back references to:
BASEDEV=USBEHCD.SYS
The section from which this was obtained is as follows:
BASEDEV=USBD.SYS
BASEDEV=USBEHCD.SYS
BASEDEV=USBEHCD.SYS
BASEDEV=USBXHCD.SYS
BASEDEV=USBHID.SYS
BASEDEV=USBCDROM.ADD /CDS:1
BASEDEV=USBMSD.ADD /REMOVABLES:8 /FLOPPIES:0
Whereas the restored backup from my T450S only has one. After adding that extra line into my config.sys file, it would seem the problem has totally gone away and that I am able to use a mouse and keyboard properly once again. I'm a little bit perplexed as to why referring to the same BASEDEV twice in config.sys would have this effect, but I am honestly relieved the solution was this straightforward.
The repeating keystroke problem is still here, but it's nowhere near as often as it was before. Everything seems to be working alright now.
I've attached a copy of the PCI report in case you're still interested
