How to clear water lines of scale and deposits

I recently replaced my master bath shower and when I turned the water back on I have very low water pressure. I bled all the air from all faucets when I turned the water back on and noticed a huge amount of crud. I turned off the water and opened up all faucets to allow the crud to flow to the lowest point and out the faucet in the basement. Still not any better so I drained my hot water heater and got still more crud out, but still low pressure. How can I clear the lines short of simply draining the lines this way?

Turning the faucets on and allowing the water to flush the lines is the best way to clear them. Start with the outside spigots and any faucets you have that do not have aerators. Then remove the aerators from any faucets that have them and flush those. Some faucets that use cartridges have screens in the them that may need to be disassembled and cleaned.

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Is the pressure low only at the new shower? Do you have the valve adjusted correctly? There are hot and cold adjustment screws on most faucets these days (to allow you to restrict the maximum temp at the shower). You may not have these open enough.

Normally, flushing the lines with water under pressure moves more crud than draining using just gravity. If the lines are so badly crudded that it restricts the flow, you may need to blow them out backwards with a compressor. Air can move through a restriction faster than water can but air does not carry the crud as well. You may need to repeat flush it forward with water and backward with air a few times. You might also mix air into the water stream into the forward direction as air behind water packs a good punch. A hard enough punch to knock a glass out of your hand at the sink.