Answer: You've identified the best way to take care of the problem, but it can be expensive and quite labor intensive. You may be able to achieve the same results, but with a little less work. Rent an aerator (the kind that removes plugs) and after running the machine over your lawn, spread builder's sand over the entire area. The sand will work its way into the holes the aerator made and over time will help improve the soil. Leave the plugs on the lawn; they will disintegrate and the soil will work its way down past the thatch in your lawn.
Best wishes with your lawn!
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