Charging Problems - Already Replaced Jack

I've got an Inspiron 5775 that's been having (increasing) charging problems for a while now. First I tried new charger cords (I've gone through three) and that sometimes made the problem better for a little (although at the cost of overheating plugs/charger area) but it overall kept getting worse, so I replaced the power jack.

When I pulled out the old one, I found that it was badly frayed, and assumed that my problems were solved!

Alas, it wasn't long before the issue repeated, and it's been getting steadily worse. If I wiggle the cord around, I can usually get a connection—but these past two days, it's been way more "miss" than "hit" to the point where I'm regularly running out of power while I'm working.

Every now and then the computer abruptly shuts down, also. I assume this has something to do with the power issue, possibly caused or exacerbated by the heat-issues caused by some of the newer chargers, because it's not like the sort of crashes I've gotten in the past on previous machines from things like failing HDDs or software problems: it's much more abrupt and irregular—but this may be an unrelated issue.

Every diagnostic I've run says that the hardware is all working fine, but clearly that's not the case. Any suggestions for what I should try next? Thanks!