If you have the company's NOC, you can transfer the sponsorship.

You can also have NOC from the Qatari sponsor.
Once NOC is signed, you can then handover the transfer papers to your Mandoob of new company, who would take all these papers to Abu Hamour Services Center located next to "Doha Mall".
Even still you face the problem, you or your Mandoob then could speak with the Captain sitting there.

Even your company is closed, you only need to have the NOC, that is all.