Since you say the soil seems compacted, I think I'd go for the aeration rather than the dethatching. It won't get rid of all the thatch, but it will poke holes in it and help the decomposition process. If you're mulch mowing, that should help get rid of the thatch, as well. There are some warm season grasses where mulch mowing can contribute to thatch, but since Marathon is a fescue, mulch mowing will help the thatch decompose. Over fertilizing and frequent shallow watering are the two biggest contributors to thatch, so if you're watering deeply and infrequently and fertilizing appropriately (especially with organic fertilizers), I think the thatch will start to go away on its own.

Grass clippings aren't thatch - so you don't need to dethatch. In general, most lawns do great with mulch mowing. However, if you have highly fertilized bermuda mowed short on uneven ground, this type of clipping washout can occur. As long as you rake it up promptly, your lawn should be fine. If you tend to have a lot of heavy rains and this becomes an ongoing problem, you might consider bagging and composting your clippings at least half the time and see how that goes. Once the clippings compost, you can sprinkle them back on the lawn and the grass will love it.

Well, perhaps me being suspect of lawn crews. Here's my thoughts; When dethatching your lawn would have left very little of the debris you mentioned on the lawn, particularly twigs. But, depends on what you call twigs, vs. my version of twigs right? Dethatching is deep raking process. If done by machine, the small branches and pine cones would be broken up more than what you saw before they did it. If they did it with a tow behind, you would seen a good deal of it piled by the mower turn areas, because the tines would generally push the twigs rather than shred, then sweep it out in the process of the turn. In general, you should see a marked thinness of the turf as compared to before. This would be immediate after the tines hit and it's raked.

Yeah, that is really terrible structure in the making. If you can,envision each crotch as being V-shaped. As the individual leaders grow and put on weight, it becomes increasingly likely that the right wind, snow or ice load will split it out there, since V-crotches usually have included bark and are therefore not strong. But nevertheless, these trees can def. be salvaged. Just do as I said above-let them grow a bit, then cut back those leaders which you are not selecting to be the main central leader. This cutting back (always to a branch, branchlet or bud) will slow these down, allowing the one you selected to remain to put on more growth and take on the job of being the main central leader. I know I said wait, but you could even do this heading-back stuff now. Just cut back to where there's a cluster of growth. Then leave it be and let it sort things out. I think they will.