Front diff is not an LSD and rarely gives trouble. If you want to replace it with an LSD Quaife is the go.
Most popular replacement for the rear is Nismo
But your problem does not sound diff related. To start with there is a thread above with instructions on how to bring your A-LSD back to proper working order if you want to try that before replacing it.
More likely you have an Attessa problem.
Check the level of the Attessa fluid in the reservoir and try bleeding (one nipple back of the gearbox and another above the diff).
Check the Attessa ECU for fault codes (dodgy sensors, faulty pump etc).
There is quite a bit of info in this section on how to rebuild your transfer box if that is where the fault lies (replace or re-arrange the clutch plates in the transfer box).