To make life easier, I opted to play LFS using a PS2 controller via a USB connector. However, since this change of control method I have found the handling to change dramatically, resulting in overly sensitive steering that feels disappointingly unrealistic - this is apparent when viewing the turning of the steering wheel on screen which seems to instantly turn to full lock. Is there any specific settings that can be changed to receive optimum realism from a controller?

First off, yes since patch X the steering has changed: see this.

second, this guide might help some.

Try reducing the steering lock (in the pits setup menu) to spread the stick movement over fewer steering degrees, e.g. from 30 to 20 or from 20 to 15, depending on the car.

You rarely, if ever, use full lock while racing.

This will result in 'slower' steering.

It's not a fix for the increased sensitivity, but it should help to compensate and maybe get you back where you were before.