Coming from a surveying background I will add a few opinions.
Depending on the age of that plat, one inch of misclosure for the traverse around the boundary is more than acceptable. Getting the adjoining properties to close this well will probably present the same problems.
It really starts to get interesting when property is valued by the square foot or square inch.
One thousandth of an acre is 43.56 square feet, or the size of a closet. Most plats that I have worked on display acreage to one hundredth of an acre.
I would have serious doubts that the subdivision was surveyed with something more capable than a theodolite and top mounted distance meter.
There is no way to tell based upon visible information what the basis bearing for the survey was, and it would not surprise me at all if the survey of the subdivision used a local coordinate system rather than a State plane system.
Carrying coordinates out to something which is immeasurable in the field will simply add to your frustration.
Input your starting coordinates to a thousandth of a foot, let the calculations take care of the rest.
Least count precision for commonly used opto-electrical measurement instruments currently available is one thousandth of a foot, or 1 millimeter, and second of angle, depending on the measurement unit in use.
Accuracy of said measurements is another matter.
GPS is another story, and given the canopy coverage of the above property, I would have a difficult time setting property pins on that property using survey grade GPS with a clear conscience without numerous redundant observations at different times of the day with different constellation geometry. Those pins would be at best within 0.10 feet of the design coordinates.
Something else to consider, the plat depicts ground distances, not grid distances, unless specifically stated on the plat. If the calculation routines incorporate scale factor for each point along the traverse, your traverse will not close. I will not add the confusion of also incorporating reduction to sea level to the mix to determine a combined factor for the calculations.
Curve calculations using radius distance and delta angle are in my opinion the simplest for most people, however the chord distance and bearing method offers several advantages, especially with regards to non-tangent curves. The curve tables I generate include all of the curve data, and this is now common.
The area above or below the chord is more easily calculated when all of the data is readily available.
In the past, curves were treated as a series of short chords within the GIS packages I used.
This introduced discrepancies in area calculations when comparing area by coordinate values generated by GIS software versus Surveying software.
This is one of the reasons why you may see Platted acreage values and GIS acreage values in the county GIS parcel data.
The P.L.S.S. (Public Land Survey System) can be truly confusing.
However at the time of its design (You can credit Thomas Jefferson) it was the best solution available, and it still works. Yes you can find significant errors in monument locations, but it gives the surveyor clues and evidence where to search.
It does not lend itself to State plane coordinate based solutions unless field work to locate existing monuments is done. I know surveyors who still will use optical instruments, and steel tapes to retrace the work of surveyors who initially set the monuments.
The B.L.M. Manual of Instructions (2009) is a required reference for those wishing to understand how public lands are, and possibly were subdivided. There are numerous versions of the Manual, and when new policies are adopted, the Manual is updated, and published. It can be very important to use the Manual which was in existence at the time of the original survey. However, for the most part, it is fairly consistent.
The gap between Land Surveying, and GIS/Mapping is getting narrower all of the time, but I do not believe that we will ever see a complete merging of the two here in the United States. Too many different types of surveying, descriptions, measurement units, and equipment used along the way to get to where we are today.
I maybe a little negative about this, but we have a long history of battling amongst ourselves.
Maybe 2022 will create a change which will help, but I have my doubts, and I hear a great deal of resistance to the proposed changes.
Just Remember, You are unique, just like everybody else!