Autorouter appears to be broken (I am using Fritzing 0.9.9.) It also appears to have changed some (there were some fixes a version or two ago) which may make things worse. So first I re aligned schematic a bit to make sure it looked correct (which it appears to be) because if it is incorrect that will reflect in to pcb.
then in pcb I did Routing->Select all traces
then hit the delete key to delete them all leaving only rats nest lines like this
then clicked on the rats nest lines one at a time and manually routed the traces
first do all the traces that don’t overlap, then consider how to route the ones that will overlap. In the end to do that I needed to reduce the grid size from 0.1in to 0.05in by clicking Routing->Set grid size and changing it from 0.1 to 0.05 and clicking OK
that allows me to route it (without any jumpers) like this. Note the 0.05in grid size was needed to keep the top 3 traces circled in red in the bounds of the pcb. If you can increase the size of the pcb you don’t need the reduced grid size.
these changes are in this sketch.
key16-1-fixed.fzz (25.1 KB)
Now a suggestion, I would replace the 1n4001 diodes with this small signal part (the holes in pcb are smaller suitable for 1n4148 small signal diode which is all you need here.
As you note autorouter appears to have bugs which probably should be reported on github, but autoroute isn’t a high priority (there was discussion of removing it during the last set of fixes) so I don’t expect anything will happen soon.
Peter