How do I find a replacement door lock for this?
If you are having a hard time finding the strikes that do not have the rectangular plate, many latchset makers have the round ones like you have in the box with the others. Seems to me that they make the bolts or latch fit into any situation. According to one of the manufacturers the type of bolt you are looking for is called a "drive-in" latch

Or as Ecnerwal suggests, although it may take longer than 5 minutes for a newbie to mortise in the rectangular ones. All it takes is a razor knife, chisel and hammer