I taught two Crappie Torney winner a thing or two 15 years ago doing this. Something none of us suspected worked even better. Learned more since then as well and will suggest you add it as well.
When Roberts cedars were real fresh we found a better way to fish straight down through them. Guys were selling welding rod rigs with connectors at both ends to do that. But we found a better way than those welding rods (expensive rigs). We slipped this kind of weight on the line immediately above the hook. Used at least 1/4 oz, but the size needs to fit the minnow strength.
http://www.basspro.com/Bass-Pro-Shops-Rubber-Grip-Lead-Sinkers/product/7565/41821 weight These come in wheels of different sizes so you could suit any minnow size and fitness condition.
This one used with the hook on the unchained bottom could have worked well also. But cut the chain slack off and use the smallest size swivel to attach the hook eye. I have also seen tunnel weights with bullet shaped ends but cannot find them sold off Basspro or Cabellas.
The minnow then had a very short leash (hook length) to spin around on. That short leash kept him lively when threatened and away from snagging a piece of limb and with enough weight underneath the rod tip. That short leash seemed to actually help get bites. Be sure to wrap the line around that rubber bone at least once to prevent slipping. That rubber tab sticking out sometimes could become an issue, but have since thought of improvements based upon my later years of other fishing methods.
Now try adding this concept to this method, instead use two bullet weights, put on the line butt to butt. The pointed ends will get you past most obstructions. Now Peg both with cocktail toothpicks (peg; as in jam wood into the weigh butt holes) (Cocktail tooth picks are the only round and pointed and hard wood toothpick I know of, and plastic T-jams are now sold). This jamming fixes the weight to the line (as in makes it continous feeling) where you want it, now part of the line system and prevents any weight slippage from hiding the feel of a hit.
For the few times that you will now get snagged, set up a heavy weight (2-4 oz.) you can snap swivel onto the snagged line.
Least snaggy swivel clip I know ofI have added heavy snap swivels to these weights
Item #1 and to these
item #2 Any pointed top weight work. If you like, put this weight set up on a second pole with real heavy line. Connect the swivel to the snagged line drop it down and pop is vigorously until the snag comes loose. Makes sure the swivel test exceeds your line weight. Hung on a secong rod you prevent losses should the hooked line break or need to be broken. This system has worked on huge baits snagged on cedar wood stumps at FF. Trick with those baits was to get the weight pulling from behind the path the bait found the snag.
Other idea have an anchor and second rod ready so you can work the first while child fishes with the second one. After a trip or two make them build the second rig so they understand the importance of keeping their line free.
Hope this helps.