lawn dilemma

We have horrendous tall scraggly dandelions among a cul-de-sac of well manicured lawns. Internet research recommends we leave the grass tall and leave the mulch in place to inhibit further growth. BUT, we also have terrible mosquitos here. There is no standing water so they are most likely living in the grass.
That means we have to cut it short and remove all mulch (which could be dark damp breeding grounds).
I did more internet research and have found a new improved mechanical way of removing the dandelions, the DLT 100. I actually was linked there from a subsidiary site to the government of Canada webpage. Apparently some mane in Montana has invented this drill bit/attachment that rips up the dandelion. It does not remove the root, but with the plant gone only the strongest roots will force a second set of leaves to get the sunlight it needs to survive. When you kill plant number 2 the root will wither away and die.
It's 30.00$ USD, plus shipping, so Dave and I are going to scour the hardware stores for something similar to try first. We'll have to buy some seed to repair the spots (and a fast growing seed will also thwart any plans the dandelion root has to grow).

Don't get me wrong, I don't mind dandelions, it's just that ours are over a foot high, and cover half of the lawn. I read all about the healing properties of the plant when research said the most natural way to combat the problem was to eat them (all 3 parts of the flower are edible, and one of the oldest known medicines). But since I let my dogs piss all over the lawn I'll leave the eating to someone else... perhaps my Mastercraft 18V cordless drill.