Measure the diameter of both pulleys and post it. The original should be 2" or just above. If your new one is within 1" then you should be able to produce enough power. You are working with a 350 alternator and 250 should be more than enough.

 

Have you checked the crankshaft pulley? There's a layer of hard rubber between the hub and the outer parts with the belt grooves. Sometimes that hardens or gets oily and can slip. Then the crankshaft pulley isn't properly driving the belts.