You have to view escort as P-47C/D only through October 1943 during which only limited escort was provided during Penetration so say Bremen, and Withdrawal support from say Bremen to the Belgium/Netherlands coast. For targets deeper than 300 miles, the bombers were on their own and the fighters had already escorted to limit of endurance - no extra fuel to drop down on the deck and free hunt. Besides orders were 'intercept and return' prohibiting chase.
When the P-38 came target support to more distant targets, then the P-51B joined - but the doctrine was still 'intercept and return' until Doolittle extended the escort role officially to seek and destroy LW in the 'air and on the ground', leading to intercept and chase and shoot up everything on the way home.
The relay system was incomplete absent range in the P-47C/D, but extended to continuous escort through target and return to R/V with Withdrawal Support when P-48/P-51 available in more numbers February/March 1944.