As I understand it, 46% of supply has already been premined and set aside for users of the old token to exchange for new coins.
What happens after the initial exchange period is over and most of those who wish to exchange have received their new coins? Where do these funds go? Who is controlling those coins?
No one controls the tokens. The address you send the tokens to during the swap is a "burn address" so the coin are not controlled by anyone and can never be spent ever