1. Make a template called 'custom_about_me' that contains the code you posted above except replace $userinfo[field15] with $profilefield[value]
2. Create a plugin at member_customfields with execute order 10.
PHP Code:
if ($profilefield['profilefieldid'] == 15)
{
global $about_me;
eval('$about_me = "' . fetch_template('custom_about_me') . '";');
}
3. Where you were going to put the code in the MEMBERINFO template, instead put $about_me.
This may require some tweaking on your behalf to get working, but I have faith