PHP Code Exploit Joomla

We have 2 joomla sites which seem to have a hack somewhere in the files. We are looking for someone who has experience in locating the hacked content and removing it. The hack, as far as we know, is sending emails via a base64 encoded hack. We require someone to find the code exploit from the base64 encoded sections of the Joomla sites and remove it with a promise that if it returns, there will be no additional fee payable - we want it all included in the same price. There will be two Joomla sites to fix. They are both Joomla 3 and have various modules, extensions & plugins and run from a very bespoke theme which has had some core files edited so we cannot just 'upgrade joomla' as the whole site crashes. Please only bid if you understand the project and can find and fix Joomla hacks. There will be the opportunity for ongoing work if you can resolve these issues for us.