Time machine won't work to install a back-up on new disk drive in old laptop

I had a fatal hard-drive crash in a mid-2012 MacBook Pro on Dec. 13 2020 and am in the middle of trying to restore the machine with a new drive in it.

I ordered a new SSD and my husband installed it. I connected the laptop directly to our wi-fi router using an ethernet cable. Then used cmnd-R on reboot to install the original system software, then upgraded it to Sierra. (I need to run Sierra due to some legacy software that doesn't handle the newer file format from High Sierra on.) All this worked just fine. Machine functions fine. It just doesn't have any of my files, settings, applications, etc.

I have been attempting to replace all my files using a Time Machine back-up and can't get it to work. We have Time Machine running on a Mac mini running High Sierra. All our back-ups are saved to an external 8TB drive hanging off the mini. The most recent completed back up is from the day before the crash, so it is probably in pretty good shape. The very last back-up looks to be partial and I believe was interrupted by the crash.

I've tried to do the restore in two ways:

A. Back-up drive connected to the Mac mini

1. 1. Launch Migration assistant
   2. First window shows shows the Mac mini -- select it
   3. The next dialogue box then shows four different volumes (one for each family member's laptop)
   4. They all just sit there with the words "Loading Backup...." for more than an hour
   5. None of the volumes can be selected and "continue" is greyed out.
   6. For a while the external drive with all the backups spins, but eventually stops

B. Back up drive connected to the laptop

1. 1. Disconnect external back-up drive from the Mac mini and connect it to the laptop
   2. Run Migration Assistant
   3. This time the first window shows an icon for each of the four laptops and allows me to select mine
   4. But the next window, where I believe I am to select which files to retrieve, shows the name/icon for may laptop at the top, but the box below is completely empty.
   5. Again, I can't continue.

After trying both of these options a couple times and digging around on the internet for advice, I'm truly stumped. I tried calling apple, but they told me since the machine was so old they can't help me. oi.

Any advice would be appreciated.

Thanks.