Roland TR-808 Bass Drum Breadboard Project

Thanks Peter! Using your initial schematic, I laid out the breadboard. I think I understand the issue better now. The underlying issue with my assumption that the schematic view and that the breadboard view understand non-polar components such as resistors or non-electrolytic capacitors.
The main issue with my prior board that was causing all the addition odd ratsnest lines is that I often rotated resistors as I would normally BUT Fritzing is very strict about the pin numbers so flipping a resistor or capacitor causes the schematic to put a ratsnest line across the resistor because it wants the original "pin" orientation to be correct exactly like the schematic.
Once I followed the schematic and laid the components in the strict way "pin wise", the schematic view stayed intact with "routing complete".
These were excellent instructions and help, I am confident these changes along with the additional part you created will bring this project to life.