Thanks. I found the problem: I had originally set the Western calendar date in cell C9 to start at 12 noon in order to emulate the Julian calendar pattern of starting the day at noon. I should not have done that.

The equation in cell C21 for J_transit also does this. I guess the person developing the system of equations was already compensating for this.

So there was a double compensation for the Julian calendar quirkiness of starting the day at noon which gave me the error of being off by 12 hours.

I have now adjusted cell C9 to start at midnight (12:00:01 am) and set cell C21 back to the form of the equation in Wikipedia and everything works.