I'm not an expert on this, but this article might help you
http://www.qatarday.com/blog/legal/no-noc-no-ban-period-the-freedom-to/2...

My reasoning is that even if you exit without exit permit, you are not allowed to return until the contract period is over. In your case, there is no contract. Even if there is one, it is for a duration of 2 months and you are in the second month.

I think you should first talk to your travel agent who arranged for your visa. They should be able to talk to the sponsor. Second you should ask your new company PRO whether it is okay to leave without exit permit and come back on their visa.

Sponsor demanding 500 for exit permit is illegal and is blackmailing you with threatening to report as 'absconding'. I think your new company can advise you on this.