The way I understand it is that you can only get the maximum contribution of a rank 4 levels higher than your current rank.
If you are rank 1, you can only get CP from rank 5. If you are rank 3, you can only get CP from rank 7 honor… etc. Honestly its going to take significantly longer to get Rank 14 than last patch, but the decay and lax of deranking means you can still gain CP while only being very close to your current ranking in terms of honor.
So its a “waste” to PVP above that amount each week. Honestly the curve seems really aggressive and I tried to balance it based on all the values given in the example post and came up with the below equation.
For the nerds, I extrapolated a curve and y = 9407.051 + 11082.26x  1943.109x^2 + 267.8953*x^3 seems to fit where Y is the Honor required to hit a rank threshold, and X is the Rank.
Rank 
Honor 
CP 
Change Factor 
1 
0.004699999999 
0 
1 
2 
7128.1954 
2000 
1 
3 
13584.9211 
5000 
1 
4 
20977.5442 
10000 
0.8 
5 
30913.4365 
15000 
0.8 
6 
44999.9698 
20000 
0.8 
7 
64844.5159 
25000 
0.7 
8 
92054.4466 
30000 
0.7 
9 
128237.1337 
35000 
0.6 
10 
174999.949 
40000 
0.5 
11 
233950.2643 
45000 
0.5 
12 
306695.4514 
50000 
0.4 
13 
394842.8821 
55000 
0.4 
14 
499999.9282 
60000 
0.34 
So basically if you wanted an excel sheet macro you would do (Rank+4 CP  Rank+3 CP)*Rank+4 Change Factor + (Rank +3 CPRank+2CP) *Rank+3 Change factor… all the way down to your current rank.
Plugging in for a Fastest Run to max would be

CP 
Rank 
Honor Required 
Week 1 
9000 
3 
21000 
Week 2 
24500 
6 
64844 
Week 3 
37000 
9 
175000 
Week 4 
49500 
11 
394842 
Week 5 
55200 
13 
500000 
Week 6 
56900 
13 
500000 
Week 7 
58600 
13 
500000 
Week 8 
60300 
14 
500000 
This matches the 8 Week to rank 14 they stated in the original post, so I am going to assume I am at least close.
Adding an edit here since I see people commenting about this a lot.
“If the player’s “expected rank” is greater than or equal to their current rank, then for each rank above their own (up to a maximum of 4 ranks), they are awarded the difference in CP between each rank above theirs and the next below it, multiplied by the honor change factor for that rank.”
Based on the item they said is that you can only qualify for the CP gain of ranks +4 to their current rank. So based on if you start the rank at “0” or “1” slightly changes things since that means you can qualify for CP at Rank 4 or 5 respectively which means you could theoretically gain 4 ranks, but besides that first rank jump there is mathematically not enough CP to jump a quad rank based on their math.
Assuming R1 is really the start and not “0” as I did the original math…
(R2R1)R2 CF+(R3R2) R3CF+(R4R3)R4CF+(R5R4)R5CF + original CR =
20001+30001+5000.8+5000.8 + 0 (starting with nothing)=
2000+3000+4000+4000+0 = 13000 which is slightly over halfway into R4.
IF you assume 0 is a rank, you lose that last 4k since +4 ranks only gives you CP from 1, 2, 3, 4. That means you can only hit R3.
Again, I am only interpretation their poorly explained system.