Have you considered building walls instead of smoothing aquifer producing stone?
This, pumping in magma defeats the purpose entirely (unless you have a volcano, you had to bypass aquifer to reach magma). In fact, magma-casting an aquifer is its on sub-type of breaching method mostly done for kicks (if you have volcano, you can bypass aquifer by digging around the volcano- aquifer tills stop a few tiles from magma vents).
You don't even need a permanently freezing biome, you just have to be careful working only through the winter. Channel out the squares and then carve out the ice+build walls. Preferably you'll build walls against the entire perimiter of the aquifer to prevent having to re-channel the ice on subsequent seasons. The main draw-back of this method is that you have to keep increasing the size of the channels at the BEGINNING layer and get smaller for each layer you pierce. For piercing 1-3 layer aquifers its not so bad, but what if you prepare for piercing a 3 layer aquifer and it turns out to be 8 layers? You have to go back to the beginning and make the first layer larger over and over and over again (unless you use DF-hack reveal to find out exactly how many layers the aquifer is). The other main drawback is that if you aren't in a perma-freezing biome you risk drowning your dorfs when it unthaws. Also, if you have more than one dorf channel, you have a very high chance of one dropping the other dorf into water that immediately freezes on exposure- instantly killing the other miner with no hope of rescue.
Alternatively, you can cheat with this method (like others) and create a drain for the water when it melts (cavern lake/edge of map drain).
Sad to say, this is by no means a new method, and in fact is one I discovered on my own accidentally. There has been an article on it under the aquifer tab in the DF wiki for years.