The fact it's on the 2.5 strain is good. Maintenance *should* be straightforward. If their custom code is giving you worries, it should be module based - just disable the modules and look for alternatives if they cause problems. Due to its modular nature, Joomla can get sprawling and a bit dauting, but it's a powerful tool, and it would be a shame to write off all the work done for the sake of it. It does take a fair bit of learning to support it though, but it's worth it IMO. I certainly wouldn't sneer at Wordpress either, but it's a lot of work to get a WP site looking good too.
Nothing wrong with Joomla if you know what your doing. Issues arise when multiple extensions which are poorly coded are used and not kept up to date.
I run 4 Joomla sites and picking the right template to give a professional look and feel is key. Joomla if used and understood correctly is one of the best CMS you can get as evidenced by the millions of sites that use it.
It does sound like the implementation needs to be scrapped and a fresh start made against a tight specification.
Have a quiet chat with SLT about your concerns. Re-iterate that you don't want it back.