I would suspect you have a heat related fault developing on the disk.
Which causes the drive to re-try reading the data all the time.
It also explains why the copy process slows down as the drive warms up, it will get more and more "read errors" requiring retries and/or head re-calibration.

Listen to the drive does it sound "normal" for a disk drive [you may have to get your ears close to the drive as it may be quiet].

If its developing a fault then replacing the drive is a good option.
If you really need to copy data off the drive then try cooling the drive [or the whole PC] down by placing it in a really cold place e.g. a room with the air conditioning turned up - you may find this lets you ghet stuff off you might not be able to.

Worst case, you may even have to put the drive in the fridge/freezer - just make sure it can't get any water/ice on it or you'll have a shorted out drive.

I did that once - copied data off a drive by putting it (running) in a freezer in the lunch room at my then place of employment - I made sure the drive was not sitting on the ice nor that any ice would melt on to it.
And it worked!