How would a starting pitcher be affected by having low durability of 13 and stamina of 86? Just more time to recover in between games or will he also tire faster during the game?

Stamina affects how quickly they tire (thus, how many pitches they can throw).  Durability affects how quickly they recover.  Generally, if their durability is 13, they'll gain back 10-15 percentage points per cycle.  So if he throws 115 pitches and gets down to 12%, it's going to take him about 7-8 cycles to get back to 100%.  The solution is to lower his max pitch count.  Without actually looking up examples, I'm guessing you need to set it around 85-90.  That should get him back in time to pitch when it's his turn again.  But you may need to play with that number.