This is confusing I know, but I do not think you need to tie it to MS account, that makes server look for underlying OS 8.1, which is not on SSD, you have DL, just try without linking to MS account. The server see's all this on your HD that had 8.1, so yes that would work with MS linked, but SSD has no 8.1 on it so no need for MSA link, you have DL, no link to MS necessary. Enter no keys, skip
The servers don't look at anything else then the hash it made/saved during the establishing of the HWID. When it's linked properly to the MSA that should able the user to move the HWID over to the new hardware. I also have replaced some hdd/ssd's and the established HWID's all still worked on the new drive, without using my MSA at all.