A well-run contest will have rules, procedures, and staff committed to enforcing the rules and procedures in the interest of conducting a fair event.
For example, at Desert Scale Classic, we've fine-tuned the classes/rules to eliminate overlap as much as possible. There's a class for every model, and very few instances where a model could fit into more than one class. We allow the entrant to place his/her model into the appropriate class, but we also monitor the placements to assure every model is in the right class.
If a model is placed in the wrong class, we ask the entrant to move it to the correct class. Before we begin judging, we check every class, every model to verify comportment with the rules. Any models in wrong classes are moved to the correct place before the judges start evaluating entries.
There are three areas out of 30+ classes where there can be dual eligibilities. In those instances, we allow the entrant to decide which placement he/she prefers, but the model must be 100% in compliance with the rules of the selected class.
I think we've seen it all, and we've dealt with it all with integrity. We've seen the trophy hounds move their models from appropriate placement into other, lesser-populated classes. We've moved them back to where they belong. Most entrants understand and agree. We've had a couple of entrants who moved their models back to the class they originally placed them in, and we've moved them again to the proper place. They forgot that we have the final word. We had one who moved his model a third time, moments before judging began. We caught it.
And, yes, we had one entrant who refused to put his model in its proper class. The model was withdrawn from competition and was not judged.
The key to preventing 'class-shopping for trophies' is to have clear, concise class specifications that prevent abuse, and then enforcing them.