My buddy is about 2,000 miles from home on a cross country trip and he just wrote me that he finally did exactly that on exactly the same trailer. He left with the bikes hanging on the ladder, which I had strongly recommended against, and he was tired of getting them on and off and he could see them swaying and bouncing around so he went to Camping World and picked up a bolt on receiver and bike rack and mounted it. So far so good he says. It should be fine. My welded on bumper has held the spare tire for many thousands of miles without falling off so I guess it would work fine with bikes hanging on it. In my case I would have to relocate the spare but you guys don't have your spare there. I say go for it.
Here's a picture he literally just sent. Unfortunately you can't really see the hitch but you get the idea.
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Paul "Poppy" Cervone
2015 Grand Design Reflection 337RLS
2011 Cougar High Country 299RKS - SOLD
2007 Silverado 2500HD Duramax/Allison CC 4x4
2007 Corvette Z51
2009 Cadillac CTS