I had this issue a few years ago when I tried to swap my 60GB HDD for a 240GB WD SSD - no matter what I tried I couldn't get burned discs to work with the SSD; I tried cloning the original drive to the SSD but it made no difference, but if you want to know how I did it, I used a Windows tool called HDD Raw Copy.
I think I remember messing about with the files on the NAND (which wasn't a good idea lol) to try and get it to work but didn't get anywhere.
In the end I just settled on using an HDD. I tried multiple during the process and noticed similar issues to you where only the original 60GB drive consistently worked; sometimes (some of) the replacements worked and sometimes they didn't, it was basically random.
I've found the most success with Hitachi / HGST drives over the years and I eventually settled on a 500GB HGST drive which I've used since with no issues. I can't remember how I got it to work, I think it just randomly decided to start working one day.
I recently took an old 525GB Crucial SSD out of my PC and thought I'd try this again to see if it would work this time but still had no luck.
I thought I'd search to see if anyone has found a solution yet, but looks like we're still waiting for a fix. There's a lot more people discussing this nowadays compared to when I first brought it up though so hopefully we can figure this out eventually.