Get dome lights with milky covers. Those that look like white paper, when turned off. Without clear "window" or any pattern. Milky cover eliminates all the weird light refraction effects of lens and doesn't create sharp shadows. Most dome lights are transparent like yours, but there are some with milky covers too.
LED color temperature the closest to "old" bulbs is 2700-3000. Called warm white or soft white. Higher numbers are more blue-ish, the higher is the number, the more blue-ish. Some cheesy-chinesy LEDs of higher color temps have pink shade, too.