The thing about lighting; especially for make up application, is it needs to be layered. Too much uplighting and you'll be doing your faces like you've got a flashlight under your chin, too much down lighting and it will have the reverse impact. Even worse, the color of your light bulbs can actually impact your foundation and bronzer process. My recommendation is to layer the lighting without increasing your footprint as you desired.
First, go mini with your recessed lights. Use nothing larger than a 3 inch adjustable gimbal trim. The small fixture will be unobtrusive, while to trim will allow you to modify the angle on a whim. Then I would install a [mirror will build in LED illumination.[(https://www.houzz.com/products/illuminated-vanity-mirror-39x28-prvw-vr~56591498) This will give you the angle of side sconce lights without taking up extra mirror space. If you want your LED bulbs to mimic natural daylight, find an LED between 4500k to 6000k. While that is closer to a cool white bulb than a warm white incandescent, you will have lighting that mirrors the day.
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