I currently have a Humminbird 535 on my jonboat.  The transducer is installed on the bow-mount trolling motor.

When I'm running the bow mount motor only, the Humminbird seems OK.  However, when I run the transom motor as well, the screen no longer reads clearly -- it's taken over by black lines and shading.

Is this interference?  Was the depthfinder not designed to read at 4 MPH?

Any ideas where to look to diagnose and troubleshoot the issue?

If the wires from each unit are laying close together it could cause the problem. Move them apart and see if this will help solve the issue. If they are running off the same battery get them as far apart as you can to cut down the interference. If you have two batteries run each unit off seperate ones. One of these should solve the problem. Let me know if it works.

Are you running two motors on the same battery?

Are you running two motors on the same battery?

No...two 24 volt systems, each with 2 dedicated batteries

Chris, I assume that your display is up front with your TM.  That means that you have a lot of excess transducer wire.  Uncoil the wire and recoil it in a figure 8.  Then, fold the two ends of the 8 together to make a 0.  This will eliminate a lot of noise because it eliminates the "antenna" effect of the excess transducer wiring.  If you have excess wiring in the stern unit, do the same.