My fitter recommended a 3mm shim under my left Look cleat to help offset a leg length difference. I'd like to get the same effect with my mtb shoes that use an SPD SH-51 cleat. As the cleat's surface is so small and that no shim is really available anyway, would I get the same effect by placing a 3mm shim inside the shoe, under the shoe's removable insole right over the cleat area? This is provided that there is enough room left in the shoe for my instep to be raised up in the upper.

I would but the shim on both sets inside the shoe. Which leg is it? And is that leg's foot smaller than the other.. if so no problem, as you should have purchased shoes based on the larger foot.
Usually people have one foot smaller than the other... I never considered one of my legs is shorter than the other.

Or just by one set of thin insoles and one set of thicker insole and use one of each.
I like this Superfeet, but they expensive.

Insoles | Superfeet

One green set and one blue set.

They make SPD shims in various sizes. Google away.

Here's just one example.

Bike Fit Systems Bike Fit Hoggs Leg Length Shims 2-Hole in Tree Fort Bikes Fitting Tools (cat1583)

^^well yes. But I wouldn't want the shim making the cleat hit the ground when I walk. Defeats () the purpose of the 2 bolt SPD shoes. In my instance I use pedals like the Shimano M324, and like to have the shoe firmly on a "regular" pedal. Putting a shim there might change engagement, or float around too much.... I don't know. Try different things until you get the right fit.