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Besides moving the site to Joomla, no, you can't do anything. I am not being sarcastic, I am being factual (unfortunately).

The biggest problem with WordPress is that it stores data in text fields as PHP serialised data, using hardcoded filesystem paths and URLs. Because of the way serialised data is encoded you can't do a simple search and replace across the database and call it a day. You have to read each row, perform a time consuming per row search and replace and serialised data structure update, then write the row back to the database. Compared to a MySQL search and replace it takes anywhere between 1,000 to 1,000,000 times as much time, typically around 10,000 to 100,000 as much time. This is the part which will take literal hours.

Joomla, on the other hand, does not store hardcoded filesystem paths and URLs and it does not store data as serialised data (it uses normalised tables, as people figured out this is the most efficient way to store data since the 1970s). That's why restoring a Joomla site takes incredibly less time than WordPress. You don't have to do this mind bogglingly slow search and replace across each row of each database table. You just... restore the database.

As long as you're using WordPress moving the site will involve this search and replace. Our data replace is one of the most efficient ways to do that (there are slightly faster algorithms —by 5% or thereabouts— BUT they break when moving the site across similar domain names). So, as I said, your problem is that you're using WordPress and there's really nothing much you can do about this. Sorry :(