Hi Richard,
First I will say that I really like the idea of where you are going with this. However, the bad news is that I dont believe this can be done out of the box without a fair amount of custom triggers (spelcode) and javascript to pick up the values and place them in the target fields on the child ticket. There is no trigger in the system to allow you to grab those fields when making the relationship between tickets as parent/child, nor is there one available when using the "close all children" function
Your best bet on this one would be to create an idea here on the community and have folks vote for it, and product management will review it for possible consideration in future versions of the product.
Sorry I cant give you a better option on that.
Thanks,
Jon I.