Interesting. Two of my 2004 alloy summer tires are both slow leaking now. I was assuming also that cleaning the rim and remounting would do the job, but maybe not. Will have to spec they use bead sealer.
May also need to be cleaned and sealed where the valve stem sits on the rim.
On my motorcycle that all had to be done, it lasted for the life of the bike. But.....
For you I'd be tempted to just go with the new rims, if they are that cheap for a set. (New though? If used maybe the same problem).