Glad you got that POS of an alternator fixed, maybe you should read a wiring schematic before asking me if I think it through, next time you post asking for help you should think before you type.
Pump
It's possible that your pump is suffering from cavitation, is this a rebuild unit aftermarket? I rebuilt my last one but found the front shaft was showing wear. Check your lines for restrictions or partial blockage.
Gauges
Rent a set of gauges and find out if system is low, there must be enough to make it cycle but won't cool. grab the low side line (large line) and feel if cold.
Alternator\Starter
My 93 truck still have the original alternator but the starter went out around 180k current mileage is 290k.
My 2003 T4R V8 starter is still original I think at 300k alternator went at 235k.