Check belt tension again for sure. Did you replace the tensioner with the pump? the belt is tensioned from a spring loaded tab built into the water pump. Im fairly certain the pump does NOT come with the new pulley/bearing assembly. SO if you do have the old one still, change it as well!
You can run the car with the cover off, however you need to remove the crankshaft pulley to get the cover off completely without breaking it after removing the two 10mm nuts. You may or may not have to remove the motor mount to take the cover off easily. (going from memory here.) This will allow you to see exactly what is causing this screeching. Obviously, make sure the tensioner is not frozen, as im guessing this, or a defective water pump bearing is the culprit (also unlikely on a reman unit, but anything is possible.)
The water pump will not be frozen, as the ‘pulley’ that drives it, is actually a gear and if it were frozen it would shear all of the rubber teeth off of the belt, which in turn would cause the car not to run due to the camshaft not spinning.
Also, coming from experience. I once had a customer who did their own timing belt on the same engine. He had a similar symptom, He installed everything correctly, proper tension on the belt, but had installed the lower crank gear backwards causing it to bind itself into the oil pump housing! And when the engine was started (At first i did a amp draw on it because it was very slow to start and it was pulling 600 amps of current from the battery!!) And when it did start it was squealing in the worst possible way.
Keep us updated and post a video if possible. I have a lot of experience with these engines and would be glad to help you out.
Here is a picture of an engine i rebuilt outside the car with the timing belt/waterpump/pulleys installed and correctly tensioned if it helps any with your repair/diagnosis.