iMac (2011, 27") freezing, unable to boot or run Hardware Test

Support Community - 

I have an iMac from mid-2011, and in the last several months it has been freezing to the point of only registering a mouse movement or action in an application every few minutes, and sometimes not booting up at all. More history:

- 2 yrs ago - iMac began slowing/hanging up/beachballing noticeably, so I maxed out the RAM. 

- Aug ‘18 - Moved cross country, and iMac worked reasonably well back out of the box.

- Nov - Started hanging up to the point of unusability. I checked the HDD using First Aid on macOS Recovery, reformatted the HDD, reinstalled High Sierra, and it worked for half a day. 

- Dec - Still non-functional, so I used OS Recovery again, but erased the HDD at the third of four levels of security (failed while trying the DoD-level HDD wipe) then restored from a MacBook backup. It worked for about 2 days, then the same issues returned & would not fully boot up.

- Jan ‘19 - Tried Apple Hardware Test 6 times with hard-wired Ethernet cable. Freezes around 90% at both normal (between 4-6 minutes in) and extended version (about 55 min in) of the testing. 

- Today - Will still not boot up fully, so no etrecheck possibility, but the below is from the Hardware Test tabs. 

Apple Hardware Test, version 3.3.1-3A225

iMac 12,2

Quad-core Intel Core i5

CPU: 3.10 GHz

L2 Cache (per core): 256 KB

L3 CPU Cache (per CPU): 6 MB

Boot ROM version: 82.0.0.0.0

SMC version: 1.72f2

Graphics: AMD Radeon HD 6970M

VRAM: 2 GB

Memory details: Overview: 16 GB, 4 GB/1333MHz in each DIMM bank

Next troubleshooting step – replace the HDD? Many thanks for inputs.