Don't know if your solution will work GM. Curious why you didn't tackle the source of the problem instead of the symptom? If the lawn sprinklers are producing too much run off, then the PR is too high and/or the system is being run too long, in addition to the aforementioned compaction.
I have a site with a small lawn that has a bad physically compacted layer at ~ 3" depth over ~60% of the lawn. The owner is not interested in redoing the lawn at this point (i.e. tilling), so I am recommending trying to bust up the compacted layer naturally. It has been a nonstop battle irrigating this area as too little water leads to brown out in the compacted areas, too much water leads to swamp and the line between those two conditions is very fine .... kinda like mixing concrete.