The problem when you connect the CD writer was probably down to conflicting jumper settings on the 2 devices.
There isn't any real way of avoiding packet writing software if you want drag & drop other than using DVD-RAM burners & RAM discs.
The Liteon really needs to use 80wire IDE cables (aka Ultra 66 , 100 or 133) for best performance.
The Adaptec (now Roxio) software was actually quite a good packet writer application & I've used it over the years without too much of a problem.
It's possible that an app called ISOBuster might be able to get the files off for you but the best option would be a temporary install of the original software.