You might improve it a bit, but you shouldn't bother.
CRI is defined by how close the spectrum is to a black body with that temperature.
Simple filters like those two in question will never actually fix any problems of the light. However, changing color temperature will usually slightly change CRI as well. This is a common trick to improve nameplate CRI slightly (in addition to tweaking of light for just 8 reference points).
Because spectrum doesn't actually get improved, your light will remain pretty horrible even if CRI seemed to get a bit higher. So, the better option is to add a coating that absorbs and re-emits part of the light, which can fix many shortcomings of the light. Generally you have fluorescence and phosphorescence as the physical mechanisms, but there are other options too - say upconverters to get blue from red light.
But it is usually much cheaper and easier to simply buy a new better bulb :)