Really bad plat
Any solution that does not take the field evidence into account is likely wrong.
It's nice when records are neat and tidy, but they are only part of the picture.
I've seen many plats like this in Minneapolis/St. Paul. But I don't remember seeing one where the lengths of the side lot lines were only given to the nearest foot. That's unusual.
With the straight lines laid out and curves superimposed, I checked 7 or 8 of the side line dimensions against the curves. As shown on this .pdf, about half of them fit the curves within a couple of tenths. The other half miss the curves by 2 to 4 feet.
Some side line dimensions might have been laid out in the field to give starting points for the curves, but others might have been scaled. And as Paden said, a variable-radius French curve might have been used to draw some of the larger-radius curves. If so, that could have thrown the scaling off.
On the other hand, the arc/chord dimensions on Lots 1-3 and 5-7 of the subject block, and Lots 18-22 of the adjacent Block 23, all check within a couple of tenths. It would have been very tedious to calculate those in 1925, which means they were probably measured. That means it's likely that the curves were run in the field, and that in turn makes it likely that curves of even degree were used. I have used even-degree curves in this calculation, as shown.
Under this hypothesis, they could have turned angles for the side lot lines from the straight baselines at the rear of the lots, and set a couple of lath on each line for sighting. In running the curves along the streets, the chainmen would have chained each successive lot frontage on an estimated line, sighted themselves in on the lath, and called out an approximate chord distance to the I-man. He would have then adjusted the deflection angle. That would have been easier to do with an even-degree curve.
After setting the corner at the intersection of the deflection angle and the lath line, the chainmen would have re-measured the chord to tenths or hundredths, since those fractional feet must have come from somewhere. They probably didn't distinguish between chord and arc on these large-radius curves.
The lot corners were probably all set, but they might or might not have been marked with irons due to their higher cost. Wood hubs would be more likely, but many of them could have been replaced with irons later.
The large curve on Lot 4 didn't have to be monumented in the field except for the PRCs at the ends. But what the field crew could have done was to measure the chord, and also set up on each PRC and measure the angle from the chord to the tangent. Dividing half the chord by the sine of that deflection angle would give the radius of a tangent curve.
As I have it calculated, the radius doesn't come out the same at the two PRCs. I get 69.78 at the northerly PRC and 70.76 at the southerly one. That means there is no single curve that would be tangent at both ends.
The field crew didn't worry about tangency. They would have given the chord length and deflection angles to the draftsman. He in turn probably settled on a 70-foot radius for the curve. He didn't have to give the radius or otherwise explain it, he just had to draw it.
A non-tangent 70-foot radius curve would have an arc length of 155.56 feet, as shown. It overlays fairly well on the curve on the drawing, and the drawing scales pretty accurately elsewhere. The 150-foot arc length was most likely a rough approximation that the draftsman came up with.
For comparison, I'm showing a curve having a 150-foot arc (radius 73.78, purple line). It doesn't fit the arc on the drawing nearly as well.
This curve is probably not going to be an occupied property line. There is no possibility of conflict with the neighbors, and only a remote possibility of a dispute with the City about the ROW location. And whatever way it's run, it would be hard for anyone to prove that it's wrong.
If I were going to bust 1925 curves, I would start by grabbing the field tables from the priod. Not many HP calculators floating around in 1925. You will probably find that things fit fairly tidy.