I think the ICL7106 and ICL7107 have the same pinout and the ICL7106 is in the MAXIM library. It has a pin arrangement on the schematic which isn't simply 1,2,3,4 ... so it should help the wiring.
However, you have some obvious problems on your schematic - no junctions. If you are using the NET command to make your connections it will automatically add junctions where necessary. It looks like you have been using WIRE which does not add them. You will have to manually add them otherwise there will be lots of missing connections.
As for the problems of wiring up all the components, space them farther from the IC. You could edit the symbol in the library but I suspect the proper symbol will work better than a 40 pin DIP symbol.
Keith