I always look on the bright side, since so many times what I thought was a catastrophe, turned out to be not so bad.
In your first video, I agree, right at the beginning of the start, I did hear a brief "heavy knock", which you could claim was bottom-end related, but it disappeared quickly. My experience with a rod knock is that it gets louder as RPMs increase. A slight rod bearing issue also sometimes won't make noise until after you just revved up the engine and on deceleration, the knock appears for a few seconds.
Th rest of the time all I heard was what sounded like noisy lifters (sort of like the worn sewing machine running) to me, along with the usual slight ticking noise of fuel injectors.
When the lifters loose oil pressure, they bleed out or collapse, this reduces valve opening, and effectively reduces power dramatically. It can take a while to get them back up to pressure. When mine started to go (on my 3.5L) we started to lose power going up a hill in drive, and started getting what I thought was spark knock, or bearing noise. When I repaired, replaced, and re-bled the lifters, all the troubles ceased and the engine is very quiet now.
Using an automotive stethoscope (or in my case a wooden dowel rod to the ear) probe the top of the valve covers in multiple locations carefully, listening for the ticking noise. It may be greater or weaker in a certain area, but if you hear the noise just under valve covers on both sides, then I would suspect lifters, or something similar. Also if your timing belt has lost tension but not yet slipped, you might be experiencing similar issues with valve timing and lifter noise.
Maybe install a mechanical oil pressure gauge for testing your pressure before panicking. See if the pressure is good, and take a peek in the oil fill hole with a light while the engine is running and make sure oil is splashing around freely under the valve covers.
If the knock is indeed bottom end noise, you should be able to hear it louder or more pronounced from under the car. Safely please, get the car up on jack stands, wheels off the ground, then listen from underneath and see if the noise is louder, I'm betting you won't hear it as much anymore.
It's also important to have the right oil filter, I usually order extra genuine Mitsubishi whenever I order OEM parts, one with the anti-drain back valve which holds some oil in place for startup. Your noise seems to fall away as soon as oil pressure builds. Be sure to use the right grade oil for your engine and the local air temperatures you are experiencing. Many Mitsu folks switch to higher weight/viscosity oils to combat the leaks or valve seal issues. I think this causes trouble with the lifters because those passages are tiny!
You may indeed end up with bad news, but based on what you have provided so far, I'm not ready to throw in the towel and give up.
Good Luck
. And all of them are quoting OEM here as per them, at least. The guys on the higher side say these is no Kit for this and all the various components come as separate line items whereas others put in a single timing kit(+ water pump) into the quote. 
