I agree with your relative scaling factor per holes played, however that does not appear to be what is going on. One stroke on a 27 hole course should count 2/3 as much as one stroke on an 18 hole course, not 1/3 as much (the current ratings are based on 3 pts per stroke for 27 vs 9 pts per stroke for 18).
Up to now the ratings have been based on averages, with no use of standard deviations that would be correlated with the non-linear scaling. Given a large enough number of participants, the standard deviation of the scores for players with ratings near 1000 could be used as a measure for non-linear corrections, just like the averages are now used for the linear scaling factor. This would not work in general due to the relatively small number of 1000 rated players at most events.