Have you re-fitted the old bottom end by mistake?
Worse compression than before!
Blue smoke suggests burning oil, white smoke is trying to burn coolant, so blueish white maybe a bit of both.
Everything you've said seems to point at head gasket, but as it's the same with 2 different blocks and new head gaskets maybe the head is cracked in a couple of places, causing cylinders 1 and 4 to burn oil and/or coolant.
Oil buzzer could be a dodgy pressure sender, but it could be that you actually have crap oil pressure.