You mentioned that you bought the extruder used. Maybe the guy before used it for abs, and was not fully cleaned, so it needs 240c to melt those abs bits in order to extrude, otherwise at lower temp the abs might block the nozzle orrifice. This could be a plausible scenario or explanation, if it needs a real 240c for extrusion. You mentioned you use black and purple pla, if it would of been clear transparent pla maybe it would of showed some impurities inside. Or you can perhaps try ask the previous owner if it printed abs with it.
Also i would try to give some insulation to hotend. My personal preferred method is to cover the hotend in a high temp silicon. This can be bought at gas stations or auto parts shop and it is "silicon gasket" for motor block or evacuation galleries and it is stable to temps up to 400C and is cheap, and has fairly good adhesion to metal surfaces. It aslo makes some bad smell first time its heated up, but after that it gets cured and its fine and odorless afterwards.
Also i would try to give some insulation to hotend. My personal preferred method is to cover the hotend in a high temp silicon. This can be bought at gas stations or auto parts shop and it is "silicon gasket" for motor block or evacuation galleries and it is stable to temps up to 400C and is cheap, and has fairly good adhesion to metal surfaces. It aslo makes some bad smell first time its heated up, but after that it gets cured and its fine and odorless afterwards.