Its all vary admirable that you are trying to calulate the nominal load while under tow, but it is not needed for the task at hand. You just need to know when it is non zero. A simple push button switch such that when the cable is under load it pushes on the switch. Design a link that come in contact under load. All the load goes to the link, and the switch detects that it is closed. A light spring seperates the link to open the contact with an empty rope. The monitor sees that the link is open and if open long enough (longest conceivable slack rope duration) and records the hight when it first went slack.

All that said, Eric's human factors solution (don't do soft releases, or say "thanks" on the radio) will avoid over charge.