First I would recommend to treat the area with a solution of vinegar and water 50/50
Go beyond the limits where you think the cat peed. Do all the room if necessary.
Repeat a few times during the following days and once you're at it I'd follow Barkingdog's advice and check for any toxic substances that could be in the basement.
Second I totally agree with you with making the main floor the cat's headquarters
Currently I live in an apartment and we have 3 cats. 1 litterbox is in the washroom and the other one in a hall. They're both covered, the ones that come with a lid or hood. We clean them once a day and we use litter deodorant and we never experience bad smells, like poo or pee, never and trust me, I have a very keen sense of smell and after coming back from work or a day out I would most definitely notice if there was a smell.
So, if well managed your husband doesn't need to worry about any smell nor seeing clumps of poop and pee since the litterbox is covered and relatively clean.
The laundry room sounds like a good idea as long as you make sure not to leave detergents, bleach and similar items to the cat's reach where he or she could knock them over and intoxicate. Aside that sounds good either there or in any discrete area on the main floor. I totally vote for that