A belt shouldn't be adjusted that tight or you'll trash the shaft bearings or bushing behind the pulley. The screeching noise may be coming from something other than the belt, like a just mentioned bushing or bearing. If the belts or pulleys have a slick glaze on them you can break it up with some coarse sandpaper...... Belt is as tight as I can get it. .....
Think of this like you just put on new disc brake pads... with a worn rotor.Maybe the sheave (pulley) is worn and it is time for a new one.
When first starting, its usually the alternator trying to recharge the battery. Is the
battery in good shape? Less than five years old? Good clean connections?