A couple of thoughts come to mind:
1. Have you checked to see that your system is purged of all air? A volume of (compressible) air in the system will force the pump to operate for a time after all taps are shut to rebuild the system pressure.
2. Could the problem with the shower be related to your water heating system? You might try running the shower with cold water only to see if you get the same results.
3. Try disconnecting the pump outlet hose and measure the pump current draw in a free-flow condition. Compare with the rated current draw of the pump. If too high, the pump could be defective.