A few things - How close together are the boxes? How often are they cleaned? By your own admission not often enough at the moment. How big are they? How close are they to noisy appliances (although I don't think this is the issue)? When was the last time they were thoroughly cleaned using bleach on the inside and outside? Most important - when was the last time your new boy was at the vet for a very thorough checkup? Including urinalysis to rule out a UTI?
Now a few suggestions to try - Move the boxes further apart so he does not feel crowded. Get another box. I would suggest a large storage box. You know the under the bed kind? They are perfect for litter boxes as they give the cat room to move around and get really comfy before getting down to business. Rule of thumb is one litter box per cat plus one extra. Clean the whole area around the boxes with an enzyme cleaner to remove the smell of urine. You may not smell it but I can assure you he can. The cleaners can be found at good pet food stores. It is quite possible one of the cats "leaked" slightly outside of the box in the beginning and now he feels that is acceptable. Change the litter to one with no perfumes. There are many out there. Perfumes are added to litter to make us feel better about the smell. It does nothing for the cats. In fact it is harmful to them. Have you tried Dr Elsey's Cat Attract litter? http://www.petsmart.com/product/inde...ductId=2751734
That sometimes works with difficult cats.
Most important, if kitty hasn't been in for a vet visit since you have adopted him and moved please take him in. It could all come down to stress from having all those changes in such a short period of time. (shelter, your moms, now your place)
I'm sure I've forgotten something. My mind's been preoccupied lately.
You'll get more suggestions soon. Good luck.