Thanks Ryan! I was able to get this to work with a few tweaks. For some reason, naming the function BaseHref didn't work (perhaps because $BaseHref already exists and I wasn't overriding something properly)...in any event, I went with MyHref and everything worked beautifully. I also added some code to RebuildStaticCacheTask.php to switch between dev and live so I can automate the refresh of the cache someday.
So, in summary...
1. Added the following function to ...\mysite\code\Page.php
function MyHref() {
if(Director::isDev()) { return "http://www.mysite.mirror/"; }
if(Director::isLive()) { return "http://www.mysite.com/"; }
}
2. Changed <% base_tag %> to<base href="$MyHref"></base> in Page.ss
3. Added the following lines of code near the top and bottom, respectively, of the function rebuildCache in RebuildStaticCacheTask.php
Director::set_environment_type("live");
Director::set_environment_type("dev");
And, voila, the correct base href for each situation. Thanks again.