Change setting name in Customizer and keep the data

Personally I think keeping your mods in an array is a nice solution, but transferring them shouldn’t be too difficult. Just loop through the array like this:

$all_mods = get_theme_mod('thefunk_theme_options'); // retrieve array
foreach ($all_mods as $key -> $value) {
    if (!empty($value)) set_theme_mod ($key,$value); // set array element as separate mod
    } 

Since you have to do this only once, when the updated theme is ran first, you may want to insert an extra check upfront and delete the array afterwards.