Cows do not burglarize houses.
Are there other less-expensive fences that can be used to secure our property from stray cows and potential thieves?
Yes, cows can be a nuisance, but they don't steal money or TV-sets...
And a normal fence would normally keep them off, unless your pool is the only drinking trough near.
I looked at the photos you shared with us.
The "View from our backyard" shows that your property borders on open fields (most likely the swamp belt of Las Terrenas). I was told that this is (and always has been) an ideal hiding place for potential thieves to monitor all your movements and strike while you or your guests are out.
Of course, a "malla cicl?nica" fence will not stop the thugs, nor would a wall in such a place (unless it's 4m high).
Nowadays you see many walls topped with razor wire. I for one, however, would not like to be fenced in like that and holidaymaker would certainly be put off likewise.
Bottom line: I do not think that your house can be made safe at justifiable costs for the time being.
Once more houses are built in the vicinity security will improve.