So far only of all image processing programs, only Relion directly supports using particles with mixed pixel sizes. Even then, whether this is completely safe or if you would see, e.g. 3D classification dominated by the pixel size difference is not well tested.
Therefore you have to match the pixel sizes somehow. It can be done at two steps - particle extraction or motion correction.
For particle extraction, you have to find particular values of raw and Fourier cropped box sizes that result in matched pixel and box sizes. For example, I had one dataset collected with a pixel size of 1.08, and another with a pixel size of 1.14. I was able to extract the first one at 456px, and the second at 432px, and by luck 432/456 = 0.9473684211 times 1.14 = 1.08 exactly. There are scripts floating around that can help you search for pairs of box size that satisfy this relationship within a given amount of error.
Really, though, the best way is to do match micrograph pixel sizes during motion correction. Because the micrographs are so large compared to particles, the spectral resolution of the Fourier transform is much higher. That means much finer increments in the final pixel size may be obtained, and also the interpolation errors are less severe. All you have to do is re-run motion correction, with a precise F-crop factor. For example, if you have movies with a pixel size of 0.84 Å and another set with size 0.66 Å, you could run Patch Motion on the 0.66 Å/px set with F-crop = 0.7857142857. After that the output micrographs will have the same 0.84 Å/px and you can forget about the difference. Just make sure they are in different exposure groups for any CTF refinement.
PS All the other parameters you mention are fine, differences are already allowed/accounted for.