Out parcel in a subdivision

Here is a nasty little problem. There is a large 1956 subdivision by a reputable land surveyor, known for his decent work. On this particular one how he determined the boundary of the section is a mystery, because he shows he set the center quarter, the south quarter, and two sixteenth corners. There is no other information given for the monuments on the section boundary.

There is an out parcel, not a part of the subdivision, which is the West half of the South half of the Southeast quarter of the Southeast quarter of the Northwest quarter.

The subdivision lots are mostly monumented, and they work quite well, so determining the lot lines is not a problem. What is a problem is determining the boundary of the out parcel. Would you set those lines based upon the subdivision monuments, or based upon a section breakdown, or both so you can compare the lines.

The section monuments today are of an unknown pedigree, and may or may not be in the same place as they were in 1956, so this is a real can of worms. It isn't my can of worms - I was asked for advice and I thought of posting it here.