The trick turned out to be not ratchet strapping it *down* but ratchet strapping it to each side rail. With one strap pulling left and one strap pulling right it's impossible for the bike to tip over.
Do look around. Don't just look at the bargain basement trailers at Tractor Supply. There are plenty of places selling trailers that are affordable.
IF you plan on ever towing on the interstates at posted speeds, your best bet is to have a trailer with decent size wheels/tires.
Be sure to buy and always carry a spare tire for the trailer.
Do place rubber keepers on your trailer tow chain hooks.
Do be sure you use a drop hitch with the appropriate drop.
Watch tongue weight and Max weight in general.
Load the trailer properly 60/40. This is even important when carrying light loads.