If you go the chemical route make sure you follow the directions. If you kill too much of the lake at one time it could DO flip then you will have an unusable lake for awhile...
That is a very good point. You could cause a crash of epic proportions. Just try to kill off enough or take out enough to give the carp a chance. But like I tell any customer, with that stuff, he who hesitates is lost. You need to nail it while it is emerging. Less material, less product, less dead material. If you wait until it is full blown infestation you are almost out of options without large risk of a total crash.