I think

(1) For exit, u need an exit permit from the Sponsor.
Tell some excuse. Or tell your homecountry to send
you a telegram informing someone is in serious
condition. This may help you to get an exit permit

(2) Since yoiu did nto do the visa processing, means
medical and fingerprints, your current sponsor cannot
stop you from coming again. If you find a sponsor,
you can come I think

I wish to add somethng more on an ethical side.

(1) If you came to Qatar with a flight teicket provided
by the current sponsor, he has evry right to reimburs
this amount form you for the flight ticket + Visa.

I am also an exptriate. but does not mean that we become "oversmart" , by making loss for the sponsor.