Forget using a PID loop, just lock to the throttle function and simplify it.

launch.ks

@@ -1,5 +1,5 @@
-run once "lib/throttle".
-run once "lib/navigation".
+runoncepath("lib/throttle").
+runoncepath("lib/navigation").
 
 parameter APOAPSIS_TARGET is 80000.
 parameter GRAVITY_TURN_START is 8000.
@@ -20,16 +20,10 @@ from { local x is 5. } until x = 0 step { set x to x - 1. } do {
   wait 0.5.
 }
 
-// throttle controls
-when TWR() > 1.5 then {
-  if SHIP:ALTITUDE > 32000 {
-    lock THROTTLE to 1.0.
-    return false.
-  }
-
-  lock THROTTLE to ThrottleToTWR(1.5).
-  return true.
-}
+// Hold throttle to maintain 1.5 TWR.
+// We do *not* use a PID Loop here because we can
+// calculate the correct value discretely.
+lock THROTTLE to ThrottleToTWR(1.5).
 
 // Main ascent control.
 lock THROTTLE to 1.0.