Alternator is still my diagnosis. It should maintain a reading at or near 140 or 14.0 volts when running. You should be able to put it under full load with little to no change...and by little I mean that it should not drop below 138 or 13.8 volts or so. This should not vary with engine speed.
The car will stay running until the battery drops down to about 11 volts or so, at that point you will not have enough to restart. Our cars do not run on the battery, they run off the alternator, the main reason for the battery is to start the car.
You might have a belt slipping, but again...this sounds typical to many many posts out here...
Search 'battery light' you will be amazed at the amount of posts with this in the title.
Again, don't toast your new battery, replace the alternator, then go out and enjoy your ride with confidence.