The only way to obtain your licence before the end of the disqualification period is to appeal to the District Court. You have 28 days from the date of conviction to appeal, otherwise you are out of time. You are able to appeal out of time if the District Court allows you, but you will need a good reason as to why you are appealing out of time.
Having said all of that, in order to get your licence back on appeal you would need to get a section 10 in the District Court. That means that whilst you are guilty of the offence there is no conviction recorded against you - and hence no penalty.
In the circumstances you have described would need exceptional reasons why you, as a P1 holder, should have your licence returned in circumstances where you were driving whilst suspended.
Regards,
Nick