Interesting. I wonder why they wouldn't want you to modify an 18-hole round with CR-Par? Seems like not doing so would adversely affect rounds where players want to play from different tees (and especially affect mixed-gender rounds).
Also I found this discussion paper (https://forums.golfmonthly.com/threads/9-hole-general-play-handicap.112202/
) that validates your methodology in all respects except one. Where you advocate calculating the CH (18/9) and CH(9) and subtracting to get the CH(X) (i.e. the CH for the extrapolated 9 holes), the discussion paper says that when CR(18/9) is odd one should always apply the extra one to the holes played by designating those holes as the odd-number handicaps no matter what it happens to say on the card (i.e. CH(9) ≥ CH(X)).
E.g. a player with SI 5.3 plays a course with 9-hole par 35, slope 125 and CR 35.5 on a day with a PCC of +1 plays to 4 over par 39 for the 9-hole round. Under your methodology the player would take a CH of 3 for the 9 holes played (0.5 x 5.3 x 125/113 + 35.5 - 0.5 = 3.4314 ≈ 3) and since the CH(18/9) comes out to 6.8828 ≈ 7 you would add 5 over par 40 to the extrapolated "back-9" for an AGS of 79 which would yield a SD of (79 - 2 x 35.5-1/2) x 113/125 = 6.780.
The discussion paper says you need to apply the 7th stroke of the CH(18/9) to the front 9 played (i.e. the 1st, 3rd, 5th and 7th handicaps if the holes played on the card are marked as odd holes or the 2nd, 4th, 6th and 8th if it's marked as evens) and so the extrapolated portion of the AGS is 35 + 3 + 1 = 39. This gives an overall AGS of 78 which yields a SD of (78 - 2 x 35.5-1/2) x 113/125 = 5.876.
So the Excel formuli should be:
CourseHandicap_18_9 = ROUND(HandicapIndex*Slope_9/113 + 2*(CourseRating_9-Par_9),0)
CourseHandicap_9 = CourseHandicap_18_9 - ROUNDDOWN(CourseHandicap_18_9/2,0)
CourseHandicap_X = CourseHandicap_18_9 - CourseHandicap_9
AGS_X = Par_9 + CourseHandicap_X + 1
AGS_18_9 = AGS_9 + AGS_X
ScoreDifferential_18_9 = (AGS_18_9 - 2*CourseRating_9-PCC/2)*113/Slope_9