All I have towed are Honda's. This procedure does two things. For the Automatic trans it will stir up the oil. Then the second will keep the battery for starting the toad charged. I have also installed the following device to help with the battery issues: LSL Toad Charge Battery Charger
The Honda battery will discharge using a Breakbuddy system while towing, plus a small charge is lost powering the clock. Make sure all electrical things are turned off, including the cruse control. Before I started using the toad-charge I had twice lost all power in my toad after long tows. Jump starting the toad on the road is not fun, but can be done.
Finally doing this every 300 miles seem excessive. I believe you can do 800 miles in one day (although this is a long day traveling with the RV) without doing the car start deal. For me once a day, when we stop for fuel, run the toad engine. Run the Honda before you start for the day, without the BB in, Run the Honda if you stop for RV fuel, Run the Honda at the end of day of towing.
I understand the umbrella deal as you need to have the Honda foot break depressed to start the car. With my CR-V I can get my foot on the break without an umbrella.
All good so far. Hope this bit of info helps.