You are assuming that parasitic draw is the culprit.
I propose that you don’t assume anything.
Did you actually charge the new battery with a charger or just drive around?
My first concern is that the battery isn’t being fully charged.
Do the headlights get brighter when you give it a bit of gas from idle? They should.
Voltage meters can be found for $10-$15.
Measure the voltage of the battery w/ the car off. A reading lower than 12.4 volts means that your battery needs to be charged.
Then measure at the battery with the car at about 20% throttle. A functional charging system will produce between 13.5 and 14.5 volts. If it’s much more than that, you can actually cook the battery which shortens it’s life. Some cars have voltage regulators. Most newer cars have it built into the alternator.
Next; are the starter bearings worn and causing substantial resistance, causing extreme load on the battery. Most any auto-parts place will test your starter if you can remove it and get it to them.