I've towed our 40' toyhauler in very strong gusty winds and felt no deleterious effects. I believe your problems with the wind causing bad handling is because you have such a low pin weight. As was mentioned even 17 percent is a low pin weight.
I can understand not wanting to double tow, or being unable to double tow, but it does appear that your solution is not a good solution. We bought our toyhauler because trying to take our bikes with us without one just wasn't working out. Sometimes you just have to look for a better alternative. It may be preferable to possible serious issues in the future. Ending up in the ditch is not to be desired.