If it were me in charge I would remove the alts from the competitions and register them as alts for that user. Then providing it isn't a huge hassle to retrospectively do this, force him/her to take the latest entry from those alts.
For example, If they made a change on one of the alt accounts after the last change on their main, it should override the main accounts pick just like it would for anyone else making a change.
The only advantage I could see from posting on an unknown alt is posting a change on the alt and then if it works out better going 'Oh, that account is my alt btw, I forgot to say'. And if it doesn't work out better, just saying nothing.
Tbh, they're lucky you're not considering DQ'ing their main imo. It blatantly goes against the spirit of the contest. Whether they are in contention or not, it gives them more chances at winning and also like you said, it takes away Top 5's from other people. Plus skews the all-times stats and the such.
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Crucifying my Oracle average one match at a time