Aphids and honeydew

I park outside under a big 30-40' tall tree. The past year or so I've noticed that my truck is getting covered in this white sticky junk every night. It looks like really light rain drops all over. This all started after Matthew tore up our tree so I thought it was something with sap. Nope.

Apparently my tree is infested with aphids and this stuff is their poop, called honeydew. To make it worse, the "honeydew" is really sweet and attracts flies. So I have like 50 flies on my truck every morning that I have to shoo away before I can open the door.

So my question is: Have any of you run into this and what is the best way to remove these guys? I'm ordering some insect control stuff that you soak into the ground and let the tree pull it up through the roots but I'm hoping there is something else I can try for quicker results.