There's nothing wrong with using the same neutral or white color for walls and trim. Just use different finishes...eggshell for the walls and semi-gloss for the trim. I know someone who just used SW's Alabaster on both walls and trim...really nice.

This might also help...

https://www.kylieminteriors.ca/the-best-benjamin-moore-paint-colours-for-a-south-facing-exposure-room/ 

South facing…my recommendation is not a light paint color. South light stays with you most of the day..well, light starts east, moves south and then to the west. But, south is the longest natural light orientation when choosing a color.

I would try B.M gull wing gray…yes it is darker, but it will stay true throughout the day and when you turn the lights on at night…still gorgeous.