Have you considered having the soles altered instead - the soles are cut, the changes made by adding a custom intervening layer, and then glued back together. There are places you can mail the in the shoe and they will do this - its on he order of $40-50 per shoe. The downside is it is more expensive, but the upside is you can chose almost any shoe you want. Another upside is the shoes will work much better physically. I have used these guys many time, but there are many others:
The can do any kind of alterations, not just level ones, but you have to spell out the dimensions to them.
You are going to be even more limited in your shoe choice if you look only for one that have the right lift to start, though they will probably function better than internal lifts.
Although 3/8" is on the borderline, any insert will degrade the way the shoe works somewhat. I maybe off-base here, but I'm guessing that the problem might possibly be a bit worse, and your doctor told you that number because that was the biggest lift you typically you put *inside* your shoe. Is that the case?
I pretty much have to do this on all of my shoes as I had a surgical ankle fusion due to an injury - apparently there were leftover parts since that leg is now a bit shorter than the other.
Unfortunately in my experience doctors, especially surgeons, but even podiatrist often are woefully lame in suggesting long term adjustments, especially for people who want to be active, and not just need orthotics to get them from the couch to the refrigerator. You may need to be more proactive in getting a good solution for you. I would a least try getting your soles modified instead once, and see if the improvement you get is worth the extra money. Another benefit you can get going that route is that the alterations can be contoured specifically for you, so there might be a much wider and subtler range of shapes as well as lifts that could help you specific conditions.
Talk to you doctor first, but you can experiment to see what works best for you. Frankly if I had not finally designed and tested my own sole modification for my condition, I never would have been able to get back to 10-15 mile backpacking days.