Are the UCG dates of the crucifixion proof of the Jewish calendar?

The UCG paper Summary of the Hebrew Calendar¹ argues that the dates from the Jewish calendar in the years 30 CE and 31 CE are proof that the Jewish calendar was in use during the time of Jesus' crucifixion. But, almost half of these dates are wrong, most importantly, the year 31 CE, the year at the crux of the paper's argument. Here are the claims that the years 30 CE and 31 CE are the only years that work for a Saturday Tabernacles and a Wednesday Passover.

Only the year 30 C.E. satisfies both needs as the year for Christ’s observance of His final Feast of Tabernacles.
Summary of the Hebrew Calendar, Page 16

We have provided a chart [the appendix]² to go along with this paper, which will show the results of such a search.
Summary of the Hebrew Calendar, Page 16

Only the year 30 C.E. will satisfy all these parameters. This places the crucifixion of Christ in 31 C.E.”the next Passover after this Feast of Tabernacles. In order to arrive at a Wednesday date for Passover in 31...
Summary of the Hebrew Calendar, Page 17

According the Jewish calendar, Passover (Nissan 14) in 31 CE was not on a Wednesday. Since Jesus had to have been crucified on a Wednesday, he could not have been crucified in 31 CE. Therefore the arguments in the paper are not valid proof that Jesus supported the Jewish calendar.

Below is a table comparing the data from the UCG appendix with 5 different sources. Additionally, the site congregationsofgod.org provides all the required math, step-by-step to calculate the dates of the Jewish calendar by hand, so every step of the math and logic used can be verified.

All of these sources agree on the dates for the years 26 CE to 34 CE for both Trumpets (Tishri 1) and Passover (Nissan 14).

The Comparison Sources used in the following table.

1. Kalendis http://www.individual.utoronto.ca/kalendis/kalendis.htm
   Dr. Irv Bromberg, University of Toronto

2. TimeAndDate.com http://www.timeanddate.com/calendar/
   Use Israel as location and Large Format (More Options > Advanced > Format > Large) to see Jewish calendar dates.

3. Harvard Math Department http://www.math.harvard.edu/computing/javascript/Calendar/

4. HebCal http://www.hebcal.com/converter/ (Gregorian dates only)

5. CongregationsofGod.org http://congregationsofgod.org/math_of_the_jewish_calendar (Gregorian dates only)

Table comparing the dates represented in the UCG appendix with the Comparison Sources.

Year	Event	UCG Appendix3	Comparison Sources	Comparison Sources Gregorian dates
26	Passover Trumpets	Friday, April 19* Monday, September 30	Friday, March 22 Monday, September 2	March 20 August, 31
27	Passover Trumpets	Wednesday, April 9 Saturday, September 20	Wednesday, April 9 Saturday, September 20	April 7 September 18
28	Passover Trumpets	Monday, April 26* Thursday, October 7	March 29 Thursday, September 9	March 27 September 7
29	Passover Trumpets	Saturday, April 16 Tuesday, September 27	Saturday, April 16 Tuesday, September 27	April 14 September 25
30	Passover Trumpets	Wednesday, April 5 Saturday, September 16	Wednesday, April 5 Saturday, September 16	April 3 September 14
31	Passover Trumpets	Wednesday, April 25* Saturday, October 6	Monday, March 26 Thursday, September 6	March 24 September 4
32	Passover Trumpets	Monday, April 14 Thursday, September 25	Monday, April 14 September 25	April 12 September 23
33	Passover Trumpets	Friday, April 3 Monday, September 14	Friday, April 3 September 14	April 1 September 12
34	Passover Trumpets	Wednesday, April 21* Saturday, October 2	Monday, March 22 Monday, September 2	March 20 August 31

[* These dates are different in the UCG appendix than in the Jewish calendar]

All dates are assumed to be Julian unless otherwise noted.

All dates for Passover are for Nissan 14 in the Jewish calendar.
Nissan 14 was on a Wednesday in the years 3,10,17,20,23,24,27,30,37,44,47 and 50 CE in the Jewish calendar. But not on years 31 CE or 34 CE.