Here's a pretty good artice on your problem:
http://infosource.uwex.edu/recorddetail.cfm?messageid=101213&heading=Garden%20and%20Landscape&headingid=2
Your question about drilling into the tree is more difficult to answer because it takes a good understanding of how a tree reacts to wounding of wood.
When a tree is injured, it closes off the area around the injury by clogging vascular tubes and forming chemical barriers around that injury to prevent decay from spreading through the tree.
This process has become widely known as CODIT, an acronym for Compartmentalization of Decay In Trees. A ggogle search will give you more hits that at a trailer park on a friday nite.
The area the tree walls off is larger than the injury itself, and the area inside the walls is isolated from the tree and often becomes a hollow cavity in years to come. Now, if you encircle your tree with several small injuries, the tree will react as if this is one big injury and compartmentalize the entire trunk. New wood will be added each year on the outside of the tree, so it will appear normal, but inside the tree will have abandoned an area the size of the trunk at the time of the injury. This entire area can rot away.
A healthy, young tree can usually take this and recover, inspite of the hollow forming at it's center, but your trees are not healthy and you're not just doing this once. You'll be back every three years reinjuring your tree.
The chemicals you are adding in these injection site are concentrated and quite hard on the plant cells in the area they are injected, so this increases the damage at the injection sites. In post mortum examinations of trees injected, I've seen areas of dead tissue running 6 or 8 feet up the trunk from injection sites, unseen from the outside, until I cut open the log.
We once were called to a site to examine some trees, one we saw was trunk injected for years. We warned the homeowner the tree was at risk of failure, and only about three days later it fell literally right on her as she laid in a lawn chair under the tree. Luckly she only suffered a broken back and recovered almost completely.
It was very interesting to see what the trunk injections had done to the tree. The entire center was punky and decayed with big pockets at each injection site.
So, spary some micronutrients on the foliage, you can do it yourself if you're handy. (Ortho sells a hose end sprayer that goes almost thirty feet, depending on hose presure). Then get some aluminum sulfate, some elemental sulfer, and apply as recommended. Then work on some longer tem solutions, like getting some peatmoss and compost down, along with some woodchips (total depth not to exceed 3' to 4").