I understand your intent... but alas..no, this will result in the same issue.
You need to match the darks and biases with the appropriate data in terms of binning (and perhaps temperature).
When you take a dark frame binned 2x2, the on-chip binning combines the information of 2x2 sets of pixels (a group of 4 pixels).
This will result in a single value of say 200. Now the original unbinned values in those original 4 pixels could have been 40,60,45, and 55 (addiing up to 200). OR
they could have been 20,80,50,50... or some other combination.
If you upsample a dark frame that is binned 2x2 with a value of 200... you probably divide the light into 4 pixels of just 50,50,50,50 (it depends on the resample method).
So you will get two different answers if you subtract with an upsampled dark compared with an original dark at the same binning.
In your example below you tried to get around it by not touching the calibration data and just upsampling the image itself. This doesn't work for the same reason. If you take a data frame binned 2x2 and then upsample it- you will again need to arbitrarily assign values to the four new pixels... these values contain the signal+dark+bias stuff. Likely you will just take that pixel and divide up the value into four. However, in the 1x1 dark frame the dark values are different in each pixel... so the subtraction will not be correct.
I suspect I am not being entirely correct in the above... the readnoise is certainly going to be different as well... since you are getting the readout of four individual pixels unbinned...but only one read hit for the binned 2x2.
Anyway...I hope this hints that you don't want to resample biases or darks (or resample data to fit a bias or dark, because that is like resampling the bias/dark and not the data..same thing)