Perhaps you might try to borrow a vax from someone of hire one. They are brilliant at not only putting a clean flow of water through things - but before things get saturated - they suck the water up as dirty water, immediately before things get soaked. They virtually wash and dry as they go. They do not dry completely but suck dry things to nearly dry so that they do not tend to smell. You can even put nice smelly in the clean water before you use it and it will penetrate and remove the wee. You may have to do this (MOST PROBABLY) on both sides and so u would be best getting the mattress on a piece of plastic on a clear floor space and literally get to grips with standing over it and giving it a good 'dollying' so to speak, in the affected area.
This is the only thing I know that may be of real help to you.
If you do this it is best for the future to get one of those plastic covers - just in case as you dont want to go through all that hard work again.
Regards
Bluebottle