I recognize the situation, but fail to see the problem.
Where is it written that post Purim and pre-Pesach there is no chometz????
There is no requirement to abstain early, or clean and kasher for Pesach 3 weeks in advance.
I love our annual ‘eat the chometz’ party. On the Motzei Shabbos a week before Pesach we invite a lot of guests and cook up all the fleishige chometz in the house and feast all night. On the Sunday we host a large brunch to use the milchiges. We’ve done this more than 30 years.
Then we just clean the kitchen and lock it up. In our case this doesn’t delay Pesach preparations as we have a separate Pesach kitchen on our second floor.