Construction pet is fairly difficult to obtain. My suggestion would be to add the construction pet chance to god statues.
Completing each god statue gives 34.4k con exp at lvl 99, which will be the largest construction exp drop and chance for pet. This update would not be seen as OP since only 5 statues (10 with monthly reset) can be made per month. Also the next best item to build is the demonic throne, which can be continuously and expensively built for 25k con exp each.