Fun topic- you're going to learn a lot as you practice with this. First and foremost you need to 'lock' your color temperature. You can easily do this by taking a grey card and placing it inside the light source area and photographing it. Then use that as a 'custom' white balance. That should compensate for any oddities in the spectral source for the light- can't tell if it's FL or LED ().

LED light sources will also (depending on the quality of the LED light) mess with the color fidelity of your objects. The 'blues' may be enhanced beyond what they look like, and the reds may be subdued because the light itself is lacking in these spectral responses. In order to fix this issue, you need a color calibration target swatch- usually a card that you take photos of at different exposures, run software on it, then get a good calibration matrix. This shifts the response colors in your image to better match what they should have looked like.

After you've fixed the color and density/brightness, then you're on to setting your objects up. You've already discovered that overexposing doesn't make a white object 'pop' off of the edge. Now you're into techniques of shooting in light tents and it can get complicated- but the good news is you're able to do it cheaply because it's digital, not film.

Some google/youtube tutorials on how to work with light tents are your best bet.

Good luck!

edit: I wanted to add that you will typically use 'gobos' or 'light blockers' to prevent light from hitting the object where you want it to appear darker. So in your 'how to make a white shoulder look dark' you're going to place a black piece of cardstock near the object so that less light reaches it.

Much of that can also be fixed in photoshop. There's a reason 'ring flash' lights work well for certain types of looks, as well. Lots to learn here- and you've got a willing model to work with :)