I don’t have any specific suggestions, except to verify that when you say towing, you do mean putting the car on a single transporter trailer and hitching it to a towball right?
Just curious and all, but why should that make you nervous? Towing a car this size (the Integra is relativley small and light) behind a 22 foot truck shouldn’t be an issue.
Reversing? If its really that hard just get help (tonnes of people will, I certainly would if I saw anybody having problems)
I would be surprised if the cost of a trailer rental from a specialist would be more than a few hundreds of dollars.