After a lot of calculations and some computer programming, I believe that the missing bearing for the roadway to the south of the lot should be very close to N 72º 47' E. From the portion of the bearing that was shown in the diagram, it appears that the last two digits are either 17 or 47, and the above bearing gave me the closest accuracy in closing the entire traverse around the lot. If the value that you get back from the assessor is different from this, then I might need to recalculate the results given below.
Once I had that, I was able to calculate the current area of the lot: 123,604 square feet, or around 2.8 acres.
There are likely a variety of points that would work to divide the lot into two equal portions. I somewhat arbitrarily selected a point along the line running due east from the intersection of the 314.3 foot and 353.77 foot boundaries on the west side of the property, and then determined how far from that corner point you would have to move to set a marker that divides the lot.
Here are three bearings:
1) From the intersection of the 314.3 foot and 353.77 foot sides: Due east, 140.447 feet
2) From the midpoint of the 200 foot boundary: N 18º 33' W, 309.86 feet
3) From the midpoint of the 80 foot boundary: S 15º 31' W, 276.69 feet
Please let me know if you have any additional questions about this.