Above all, I'd expect the dimension to be along the line which establishes the location of the point.
Notably, your screenshot shows that the 12 figure is longer than the 300. That makes no sense. And since the 12 figure is not established as an offset of the circle, it should not be indicating that it is. (But it does indicate that.) And the 300 is shown as the length of a chord. (It is not a chord; it is a tangent.)
The 300 on the right side of your screenshot should be either along the green line or along the red line. (Probably the red line, in my view.) The 12 should be perpendicular to both the red line and the green line, at that terminus of the 300 line.
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Further, as I said in the original post, I think there should be at least an alternative option (perhaps not getting rid of this observed behavior) that would yield a different solution.
The following is the solution when only using options that arc elements provide:
I also provided a line tangent to the circle at the point where the arc element begins. It is 300 feet long. The element at the end of that 300' segment is 20' perpendicular to it, which coincides with the PC of the arc.
Here's what I expected to get:
So, obviously I know how to construct something like this, assuming I know where the variable offset should begin. If that hasn't been established, then the solution will have to be by trial and error.