Haha! Wasn't it evil to translate 'porneia' as "immoral" and let the anxious Christian mind fill in the imagined definition. So you process the Jesus teachings and end up with…masturbation.
The "body" would not be your lone physical organism. The "body" is the corporate body of believers (1 Cor 6:15, 10:17; 12:20; 12:27; Eph 4:25; Rom 12:5).
Paul's discussion is about whether Corinthians can go to pagan temples, which were centers of commerce and politics. Paul thinks a spiritual contamination will occur, especially from eating meat sacrificed to gods.
So I guess it does get back to beating the meat.