Any ideas of possible differences between sector-by-sector cloned disks?

The applications may be looking for a specific drive. Serial number or similar.

I'm assuming the vendor no longer exists?

In the meantime, if there is important data on this device, backup twice if not thrice.

This might be involved, based on the possible age of the system. The original LBA system for accessing HDD's used 28 bit for the LBA address. Given that one Sector is 512 bytes, that comes out to a max size of the HDD of 137 GB in decimal values, or 128 GiB in hexadecimal measurements the way Windows does it. The newer version of LBA raised that to 48 bits for the LBA address, capable of a huge number of Sectors - more than we may ever see on a rotating-disk mechanical drive. That became common just around or after year 2000. All current HDD's etc. support the 48-bit LBA system.

If you are using an older computer with only the original 28-bit LBA support in its BIOS, you can NOT install any HDD over that 128 GiB size. If applications believe the HDD is larger and will allow use of space above that boundary, the OS still will not be able to send an LBA value over the boundary. Thus it is possible for data to attempt to write above the boundary, but actually get written to a very different location, corrupting the old data at that location. So in systems like that, any replacement HDD MUST somehow be limited to behaving as if it only has 128 GiB of space. Seagate used to have a utility for imposing that limit on its HDD units, and I have used it with success. What you did with hdparm sounds like something very similar.

So, my hypothesis is that in using a modern storage device you ended up with a unit that can access space over the 128 GiB limit. Even if you set up its Partition to no more than that and left the additional space Unallocated, there might still be a problem in using such a HDD in an older computer with only this 28-bit LBA Support. Hence I suggest that a current HDD MIGHT be used if you can change its own parameters so that it believes AND reports to any outside inquiry that is real max size is not more than 128 GiB. I don't know how to do that using a SSD, although surely one that really IS less than 128 GiB should do the job.

Yeah, I neglected to think about the HDD access mode. A machine that old knows nothing about SATA, and will use only an IDE protocol. Now, what that does when used on a AHCI device I don't know. In current computers that have both types of ports, there is no easy way to access a SATA unit from an IDE port to find out. But I would not be surprised to find that, when the BIOS runs its POST and the initial identification query to the HDD unit is carried out, the response from a SATA drive may contain data the BIOS cannot recognize. Then it would no know how to deal with that storage device.

It is also possible, if that system is even older than I thought, that its BIOS does not know how to use LBA properly, and it requires specification of the even older CHS parameters to use a storage device. Do you recall how its HDD parameters were set up before you started? If that were the case, I don't think there is any way to enter CHS parameters for a modern HDD. That tasks may be left to an adapter, but your adapter seems unable to do that - or, at least, can't for an SSD.

Given what you now know, I suggest your best path forward is not to attempt to use an SSD in the old machine. Use an HDD. It may be VERY hard to find a new one that is not over 128 GiB ("137 Gb"). Moreover, ideally you should get an with an IDE interface so you don't need an adapter. I found these two examples. Both are end-of-life devices represented to be new, but with limited warranty coverage NOT from the original manufacturer.

https://www.newegg.com/Product/Product.aspx?Item=9SIAAEE3XR1053&cm_re=IDE_hard_drive-_-22-144-102-_-Product
That one's a WD unit of 80 GB.

https://www.newegg.com/Product/Product.aspx?Item=9SIA5AD1T69209&cm_re=IDE_hard_drive-_-1Z4-002P-00009-_-Product
That's a 160 GB Seagate product. Too big. I think. BUT if you download Seatools for DOS and burn it to a bootable CD, you can run it on a newer machine and alter the configuration of this Seagate unit before trying to put anything on it. The tools in that package include two for limiting the apparent size of the unit. One can allow you to limit its size to the maximum number of LBA addresses it will accept. To fit into the 128 GiB limit that is 268,435,456 (2^28). The other limits the device to 32 GB for earlier machines. I don't know how to do that latter change on a WD unit, but maybe they can tell you how to use their disk utility software for that kind of job. Either way, you should be able to make some reasonably recent HDD behave properly in the old machine. Once you can do that, you can clone the old data to the modified new unit using a new machine but insisting on a MBR Partition system and a Format using FAT32 rather than NTFS. That combination should work in the old machine.

Thanks for those details. So you did get the revised system to work as you need. Congratulations! Dealing with obscure mis-matches among different technologies from many development periods is always a huge challenge.

As an example. I have a friend who's a professional librarian by training. He has shown me documents dealing with the problems of trying to preserve data and information so that it can continue to be accessed as our storage and retrieval technologies change. It's a nightmare! Not only do the technologies change, but many have much shorter lifetimes than we have been used to in the past, making data disappear by corruption due to age of the medium.

Your particular situation is all too common. So may industries have computer-based systems doing critical functions that have become very old and started to fail. Yet nobody really has any records of how that system was designed (what was the basis of the software?) so that it can be replaced with a new set of tools that duplicates the functions of old ones. And in fact, many firms caught in that bind are shocked to find out how much such a re-development project might cost! It is nowhere near as simple as replacing a 40-year-old AC motor.