If I'm using amchur primarily just for the tanginess, are there any good substitutes? I'd rather avoid things like lemon juice, since often it's very convenient that it's a powder, not a liquid.
Amchur doesn't give much of a flavor other than sour, at least, not in the amounts I use of it. It does have a bit of a distinctive aroma, but really, to me, it is just a fairly neutral sour flavor.
The easiest, most neutral substitute would be citric acid powder. Unfortunately, they don't usually give concentration/strengths on the packaging, but comparing Ball Citric Acid for Canning to the powdered amchur from the Indian store, it's pretty close. I think the citric acid tastes a tiny bit lemony, but not enough to make a difference.
Also, the amchur powder I buy is generally quite finely ground, and the citric acid is generally in crystals. If you are doing something like a spice blend (e.g., chat masala powder) you would probably want to grind the crystals up to match the texture of the rest of the spices.
Depending on what you're making, there are quite a few substitutions, but most of them would be more obscure than (or at least as obscure as) the amchur, and all would be less neutral. Also, amchur is dry, so adding something liquid might affect your recipe. (Easy to adjust if you are adding to something liquid, of course.)
In many Indian dishes, most of the Indians I know simply do use lemon juice when they want to make something sour, especially for northern dishes. This really is quite common, and nearly every Indian cook I know in the US has a large bottle of lemon juice in the fridge for every day use.
If you're making something South Indian, tamarind pulp or paste is often the souring agent of choice, but it is distinctly not neutral. It has a distinctive flavor and will also darken things (in a somewhat yellow-orange-brown range).
Some regions also use dried kokum fruit in the same way (classic Maharashtrian aamti, for example), but I would say it is even more distinctive than tamarind, and it also will darken it (with a dark grey-green-brown range of color).
For both kokum and tamarind, you soak the pulp in water and add the soaking water without the pulp to the dish. You can also usually find tamarind concentrate (a tarry paste) but I've never seen anything like that for kokum.
One more option I just thought of is using some other unripe or sour fruit. Amchur is made by powdering dried green mangoes. You can actually sometimes find dried green mangoes at places like Trader Joe's and if it is unsweetened, a small piece of that can certainly be used, but it seems that any fruit that is firm and sour should work, such as an unripe plum or a very tart apple. In that case, I would suggest either cooking with a small piece or two of the fruit in the sauce (if there is one) and removing it later or you could try to crush it and press some juice out. The problem here would be in figuring out the correct amount to add, but I think you could start from the dried-to-fresh conversion rates for herbs.
I also use crushed dried pomegranate seeds for tangy flavours in Indian curries. And once cooked, you don't get the crushed texture, rather smooth curries.
However, for making mint chutney, I use fresh green mangoes and I understand that they do have liquid content in them, but pulp as well, which balances out the liquid.