BiB - Argenta demonstrating overalls back inside t-shirt
An anonymous fan came with this elegant solution: wear a t-shirt under the overalls, but put the straps in the back under the t-shirt, while the bib in front is outside.

To demonstrate this idea, I made a mini photo shoot with my inflatable mannequin, who I call Argenta. I have put her in a pair of vintage overalls that I had not used before in a photo shoot, because it has a rather small waist; too small for the models I have used until now. But the mannequin is of Asian proportions, and it fits better on her. At first the regular way of wearing the overalls:
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Then I put the straps in the back through the t-shirt and out through the neck opening, so they are now worn under the t-shirt, while the front bib is still on the outside. Now the straps can't be pulled off the shoulders anymore, and after adding a padlock on each buckle, both the overalls and the t-shirt can't be taken off anymore.
I was surprised how normal the back still looks, so I'm convinced that if you manage to secure the buckles in a non-conspicuous way, like I tried to do by hiding the red padlocks beneath the straps, it would not be very noticeable in public.
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Note that this solution won't work with overalls that have high sides (unless perhaps with a crop top), or e.g. with straps attached to the bib sides instead of the back.