Would getting a 3rd party IDE adapter just solve all this?
No, it won't. It's a bug of HDToolbox which is independant of the controller.
Check the drive's label. There should be something like "LBA" or "user sectors" printed on it with a very large number. For an 80 GB drive it should be around 156,250,000.
In HDToolbox go to "initialize drive" and increase the number of cylinders until the "total number of blocks" matches the LBA value.
Bye,
Thomas