How can I adjust my IC placement further to route properly?
First of all, the autorouter is awful. I suggest you lay out the ICs more closely, with the sides that have the most common connections facing each other (meaning if two sides of an IC have many connections, put them side by side to lessen the length of your traces.

It looks like you may be running traces to connect the GND pins. While this isn't inherently bad, you'd want to use a ground pour (use the polygon tool to draw an area around all ICs and name it "GND") to kill the need for those traces and open up the layout to allow you to run more traces.