Nikon D5300 video, get a Sony a6000?

[TASOS PAP.]

PROBLEM guys. I've been a longtime user of Sony a3000 (mirrorless) and I decided to get a DSLR, the Nikon D5300 with the kit lens. But, I was very disappointed by the low light video, with it being very underexposed. In Sony a3000 despite the high noise (which was a result of the sensor's low sensitivity max) I never met underexposed video in low light and, even when I zoomed, the loss in 2 f-stops of light was not even noticeable. In D5300, zooming gets all the frame dark in ISO less than 3200.

I shoot in ISO 1600 in both cameras, max aperture available and 1/30 shutter speed.
Do you consider getting a 35mm lens would solve the problem or should I get a Sony a6000?