Being pull-up resistors they would provide a source current.
I'm not sure what you mean by "original recommended" but there is no such recommendation in the I2C Bus Specification, and hasn't been since at least version 1.0 (1992) when fast-mode was added. There are a series of charts provided for determining the min and max values based on speed, supply voltage and bus capacitance. The minimum specified sink current for devices supporting standard-mode (100 KHz) and fast-mode (400 KHz) is 3 ma. Therefore the minimum pull-up resistance for a 5V system would be ~1K5. The maximum resistance depends on bus capacitance. Assuming 100pF bus capacitance, the maximum resistance for fast-mode would be ~3K5. 4K7 would be okay for a bus capacitance of 250pF in standard-mode but only 70pF or less in fast-mode. Even then you wouldn't choose the max resistance, but rather the mid point of ~3K1.
Therefore in a 5V system supporting fast-mode with a bus capacitance of ~100pF the optimum value for pull-up resistors would be ~2K5. (All of the ops devices support fast-mode).
My recommendation of 1K was for devices supporting high-speed mode (up to 3.5 MHz) where the min sink current is 20ma. But I see now that the ATMega only supports fast-mode.
In summary, the op should be using ~2K5 pull-up resistors.