Popping out the exhaust is due to a lack of back pressure and a lean low speed fuel mixture. It won't hurt anything, just annoying, but normal for unrestricted exhaust. Some carbs have what's called an
air cut valve on the side of the carb. It cuts the air to the idle circuit to enrichen the mixture during decelleration to
reduce (or eliminate) backfiring out the exhaust. Your carb doesn't have one. Having the stock carb might help.
By the picture, your carb has a fuel screw. If you were to take it completely out, you might find it is missing something. It is normally "held" in place by a spring. Many times people remove the screw and lose the spring. Find out what kind of carb it is and a replacement may be available.
Jet kits are worthless. Just take the carb off, take it apart and see what kind and sizes of jets are in it. To buy a jet kit, you need to know what kind of carb you are working on. See the thread
Carburetor Basics ( Thanks to Saber6) - it will explain it all without me having to echo it.
Hope this helps. Worse come to worse, you could send the carb to me and I could check it for you.