I think you confused something. If you want to change the column number, you don't have to do anything with subcategory.html.
Well I examined the core code, and it's possible to write a plugin to change the column number (one of my plugins already has something similar feature). The problem is that in both home & category page, the categories are displayed through site_html_print_cat, so you can only change column number together on them (until you don't change this behaviour, using a plugin).
It seems there may be possible to write a global to call instead of <%category%>.
Basically in the global, you should implement a code similar to site_html_print_cat code or use the category_loop to build your own category list.
For home.html page you can set 3 column mode with Admin/Setup/Build Options/ change 'build_category_columns' option from 2 to 3.
And on category.html, you list your categories in 1 column using the suggested global.
Sorry, I'm busy now, so I can't write it for you, but if you start developing it, and you get some problems, me or somebody else will give you some advices & help in your development.
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