This might be an interesting situation in which to look at under-counter or even toe kick lighting for your work table in the kitchen. Overhead lighting from cans can sometimes come across as harsh, so if you had your linear light on over the dining table, then you could turn on softer light from underneath the work table at lower levels for ambience if you wanted and get some illumination in the kitchen while you are eating. Depending on your kitchen dimensions and the size of the can lights, you might need more than just one. I ran across the greatest overview on how to plan lighting from the manufacturer Juno. This link is from one of its vendors, Green Electrical Supply, and talks about how to plan placement and number of lights in a kitchen area: https://www.greenelectricalsupply.com/Juno_Lighting_Techniques_and_Planning_Tips.pdf