i would not be so quick to replace the starter just yet
this 'slow start' symptom can be caused by things other than the starter itself.

if your getting any chattering or clicking on the starter solenoid?
then the problem could be in the wiring control circuit as well.
and by all means please do check the alternator output to make sure its charging the battery.

The reason your getting the high amp draw across the starter is that it is trying to compensate for the voltage loss, this will ultimately burn up the starter if the real issue is not repaired soon after it starts happening.