You need more oxygen in your lips.
In classic Dr.Mark style, this statement is highly accurate, but we don't have to go to the dark side (of trombone equipment) to achieve success. Getting oxygen to the lip is a physiological process, not an equipment fix. Blood flow is essential, as that is where the oxygen is found. In so doing we optimize aerobic metabolism. However whatever size mouthpiece you use, and what ever pressure is used, blood flow will be diminished into the region behind the mouthpiece. The bigger the mouthpiece, the bigger the region involved. So to correct for these mechanical responses: massage the lip often. This gets the lactic acid out (from anaerobic metabolism that results from the blockage of blood flow) which has it's own damaging effects, and minimizes swelling to enhance blood flow (and as you stated, enhances "oxygen delivery") into the tissue.
Hope this helps.