We have had a couple of issues in the 15 years we have been racing JF with tow straps, but only two, and that was the dragster driver was not paying attention. It helps when we have crew members on the tailgate of the tow truck to watch the strap.
Back in 1969 I used a tow bar that attacked to the front axle , lifting up the front end and a trailer hitch coupler on the other end and just towed it back, even at the US Nationals when we won the event. We also just had 1 or 2 crew. Wide-open you might want to build such a tow bar, you don't even need a driver in the race car with the tow bar. Just have to design the bar to work around a nose piece. You could tow to the staging lanes, take the bar off , leave it on the tow truck, race and come back to pick it up, alto if you have just one crew guy, he can drive to pick you up at the turn off.
Here is a photo of the dolly we use now for just moving the race car around in the pits and by lifting the front end up we can load the car into the trailer and then lower the car down onto the chasis support in the trailer.
Cheers, Jon