First make a backup of your entire site or all the files you have modified (keep them safe on your computer in a separate folder and keeping the path). Then try the following, it should work because that's what it's made for:
1. Copy all modified files with their parent folders from com_ onward into the templates/ut_binv/overrides folder. and it should look like this: templates/ut_binv/overrides/com_contact/contact/default.php, templates/ut_binv/overrides/com_users/profile/edit.php, etc
2. Edit the file that is inside overrides example: templates/ut_binv/overrides/com_contact/contact/default.php and add any text, refresh the frontend and verify that the added text is displayed, if it is displayed it means that your files they are being loaded from TEMPLALTES/UT_BINV/OVERRIDES, this means that they are being loaded from the right place, because these files are yours and are not modified when the plugin or template is updated. Remember this is good to have a copy off site in case disaster strikes.
3. Remove added texto to test.
Regards