1998 Honda Accord Battery Load

I just replaced the battery in my car. The new battery has a higher rated CCA than the original factory battery that it replaced, 550cca vs 800cca.

I work on the road a lot and use my laptop in the car. The laptop has a 90w power inverter that takes the 10amp power from the cigarette lighter and converts it to DC 12v for me to plug the regular laptop power supply into. The power supply brick from the laptop is a 65w supply, so the inverter will supply more than enough power

After the replacement of the battery, the inverter now beeps when the laptop is plugged in which indicates that the cig lighter is not supplying enough power when the car ignition is in the accessory position. The new battery has 800 CCA, and was tested by the installer about 2 weeks after installation at 892 CCA. I was told that the battery was fine. I took it to a parts supply place who also tested the battery and was told that the alternator is definitely putting out about 13a and was fine, but when a load was put on the the battery, it indicated that the battery was bad. I'm not sure which to believe and not sure what to check next. Obviously, if I start the car, the power inverter stops beeping and the laptop receives enough power.

I need to run my laptop from the car cig lighter without having to start the car every few mins to stop the beeping. I never had a problem prior to the battery replacement, but realize that it might be just a coincidence.

Any ideas on what it could be and what to try next?