I think I figured out internal Vcc measurement (so we can remove R1/R2).

Its all in 17.13.1 (page 134) of the datasheet.

The only required ADC-configuration change is to set the ADMUX register to use Vcc as reference voltage. (Note this configuration will give a 10-bit result, to be read from the ADC register.):

ADMUX = b00001100;

If we want to read internal temperature, ADMUX need to be set back to read ADC4 with Vbg as reference:

ADMUX = b10001111;

…and we then alternate between the two configurations with a small time delay after each change. Possibly we also need to read the ADC twice each time, to get more accurate results.

To figure out the ADC result for Vcc:

adc_result = ADC;    //16-bit integer

where adc_result = (Vbg / Vcc) * 1024;
= Vbg / (Vbat - D1) * 1024;

where Vbg = 1.1 V
and D1 = drop over Schottky = ~0.25 V

So adc_result = 1.1 * 1024 / (Vbat - 0.25)

The typical lookup table we use will look like this for Vbat:

4.2 V = 285
4.1 V = 293
.
.
.
2.5 V = 501

Note lower Vbat gives higher results (Vbg becomes larger as a percentage of Vcc). This would also be an opportunity to finally upgrade to 10-bit ADC operation.