I knew a friend. She went on vacation and never returned back to Qatar. She then applied and worked at UAE, but since her RP in Qatar still valid, her UAE company sent her back to her employer in Qatar to cancel her RP here which she did and went back to UAE and obtained the RP there.

I think same thing can happen to you, your Qatar employer will send you back to Oman for RP cancellation, of coarse with a job offer in your hands, so your Oman employer could believe you and will agree to cancel your RP.