Problems with our four different cats

Four cats own my wife and I. Nugget, ex-female, delcawed, 18 year old
tortoiseshell, who is hyperthyroid, very thin but active, and on
hyperthyroid pills; Scrap, ex-male, declawed 11 year old domestic
shorthair; Smoke, ex-female longhair with claws, 3 year old; and
Freddie, ex-male, 1 year old with claws, who apparently was abandoned,
with congenital respiratory virus causing intermittent sneezing with
mucous and some occasional wheezing on strenuous activity - on
molasses-like goo food supplement to build up immune system. His
sneezing will never be cured but does not inhibit his activity or
appetite, which is tremendous.

The main problem we have is that we have four litter boxes, using Tidy
Cat. 3 boxes are in a row, the one remaining is across the room by
itself. Someone is urinating outside the row of litter boxes, and
outside the isolated one. No matter how frequently I empty the litter
boxes or change them, the behavior does not change. I have no way of
knowing who is doing the bad behavior without uninterrupted
observation of several hours duration. I could use a hidden camera,
but how expensive might that be?

The only thing I can think of is that Nugget, the oldest cat, might
not make it to the box quickly enough and wets outside the box. But
the most likely scenario might be antisocial behavior.

Can anyone offer any help?