Keyboard Issues - Ghost Scrolling - Can't Reset PRAM

I have a Mid-2015 15" Retina MacBook Pro. The user complaint was something to the effect of the "trackpad is behaving weird". Based on that I suspected maybe it was a swelled battery issue or faulty trackpad which I have seen before. But it is none of those. Battery is fine and trackpad works. I might need to post a video to show you what this is doing but I'll try to explain it first.

If I open Safari and start to type in the search bar, all is good unless I start with an "o" or an "L" in the first few letters. As you type, a drop down list appears with autofilled "suggestions". When I get to an "O" or an "L" it starts scrolling rapidly up and down the list, almost as if someone is pressing the down cursor key. I have also discovered that while this is going on, if I mouse up to the menu bar and click on the Apple menu (or File or any of them), the cursor will start cycling down through all the menu items. I think if I press ESC it stops momentarily but that's it.

Here's what I've tried (none have made any difference).

1. Open up Notepad or TextEdit and type. All keys type as they should.
2. Reset the SMC - this appears to work. Light on charger goes from orange to green and back to orange again. Good, but no difference.
3. Reset the PRAM - For some reason, I am unable to do this. When I power on the MacBook it seems to take a ridiculously SHORT amount of time for the Apple logo to appear. On other machines I've done this on there is usually a couple second delay between the startup chime and the Apple Logo - not with this machine. It chimes and then milliseconds later the Apple logo appears. I also tried just holding option to boot from another device - NOPE. I can't even hold D or R or cmd-d or cmd-r to boot to recovery mode. No matter what I try it just immediately starts to boot. I even tried swapping out the SSD with another one with fresh macOS on it and it does EXACTLY the same thing. I also tried sudo nvram -c in terminal but if that does the same thing as cmd-opt-P-R then that did not fix the problem.
4. Tried a USB keyboard - NOPE, same behavior.
5. Opened the Mac and disconnected the keyboard, inspected it for corrosion, and reinstalled it. - NOPE same behavior.

What can I try next? I'm out of ideas? It especially concerns me that I can't zap the PRAM on this machine. Is there a way to block this in firmware that I'm not aware of? And if so, how do I unblock it?