Photo and video color matching with same camera advice

Hello everyone!
I'm here asking an advice since I think I tried everything.
occasionally I deal with catalog photography of small objects.
I own a nikon d-3300 with a 17-50 sigma and adequate strobe lighting.
the *fundamental* thing for me is to have pictures with realistic colors of the products that will then published on the web.
it does not matter if the user who sees them will not have a calibrated monitor, the important is that the image provided has correct colors.
periodically I perform the monitor calibration / verification and camera color profile calibration with the classic colorchecker, applying it on lightroom.
as for the photos, I have no problems: the colors are realistic and I am satisfied.
the fact is that now I need to make some very short films of a few seconds (I have and use enough continuous incandescent light).
naturally I gauge white with pre-measurement when I switch from strobe to continuous.
problem: the colors do not match to the photos, even after calibration with the 3d lut creator for premiere and the colorchecker.
the video colors are so different from the photo that it seems that not even the calibration can correct them.
the video doesn't even seem remotely close to the photographic result, very little vividness, a disappointing result.
it looks like it was shot with another camera.
now, I realize that the d-3300 is not a modern camera (at least for the video part): it seems to handle the photo and video part in two completely different ways and that the video function is more of an extra than a real feature.
what do you recommend to obtain same colors in video and photo?
another camera?
a mirrorless (using the sensor always in live I assume that photos and videos colors are identical)
what else?
I have no experience with video so I ask you for sincere advice!
Greetings to all in advance!
I'm here asking an advice since I think I tried everything.
occasionally I deal with catalog photography of small objects.
I own a nikon d-3300 with a 17-50 sigma and adequate strobe lighting.
the *fundamental* thing for me is to have pictures with realistic colors of the products that will then published on the web.
it does not matter if the user who sees them will not have a calibrated monitor, the important is that the image provided has correct colors.
periodically I perform the monitor calibration / verification and camera color profile calibration with the classic colorchecker, applying it on lightroom.
as for the photos, I have no problems: the colors are realistic and I am satisfied.
the fact is that now I need to make some very short films of a few seconds (I have and use enough continuous incandescent light).
naturally I gauge white with pre-measurement when I switch from strobe to continuous.
problem: the colors do not match to the photos, even after calibration with the 3d lut creator for premiere and the colorchecker.
the video colors are so different from the photo that it seems that not even the calibration can correct them.
the video doesn't even seem remotely close to the photographic result, very little vividness, a disappointing result.
it looks like it was shot with another camera.
now, I realize that the d-3300 is not a modern camera (at least for the video part): it seems to handle the photo and video part in two completely different ways and that the video function is more of an extra than a real feature.
what do you recommend to obtain same colors in video and photo?
another camera?
a mirrorless (using the sensor always in live I assume that photos and videos colors are identical)
what else?
I have no experience with video so I ask you for sincere advice!
Greetings to all in advance!

Thanks for the reply sausage.
Colour balance doesn't solve this, I tried neutral, vivid etc with small improvements but the problem still exist.
A friend of mine pointed out:
- the difference in colorspace that video mode uses (not sRGB) in respect the photo mode,
- the fact that the camera I'm using can't film in raw mode,
- the fact that the videos are shot just at 1080p and are compressed with H. 264
All this things create the issue I'm describing...
Colour balance doesn't solve this, I tried neutral, vivid etc with small improvements but the problem still exist.
A friend of mine pointed out:
- the difference in colorspace that video mode uses (not sRGB) in respect the photo mode,
- the fact that the camera I'm using can't film in raw mode,
- the fact that the videos are shot just at 1080p and are compressed with H. 264
All this things create the issue I'm describing...

If your video cannot match the 'still' image can you match the 'still' image to your video? Otherwise I suspect that you would need a good piece of software to manage the colours (Something like Premiere Pro) - although I do wonder if folk actually do expect video and still to look the same?
Although personally I would say that the amount of time you are spending on trying to get them right, it would maybe best to purchase a camera which has truly both functions working well. Sony Mirrorless I can recommend.
Although personally I would say that the amount of time you are spending on trying to get them right, it would maybe best to purchase a camera which has truly both functions working well. Sony Mirrorless I can recommend.

Quote:- the difference in colorspace that video mode uses (not sRGB) in respect the photo mode,
- the fact that the camera I'm using can't film in raw mode,
- the fact that the videos are shot just at 1080p and are compressed with H. 264
I'm not an expert on video, but yes, I can see that those factors could make a difference. One other thing that comes to mind is the two different light sources, for example are the lights you are using for video full spectrum?
Tungsten incandescent AFAIK have been largely replaced by high CRI LED's.