I expect that if the rule is in the "private world rules" section of your world, WiS will honor it. Be polite and very specific when making the request, make sure you remind them of your private rule in the ticket to change owners, and it wouldn't hurt to have the new owner also submit a ticket stating that he understands that the record from this season will be on his permanent WiS record.
It might or might not happen over the weekend, but if you get the ticket(s) done over the weekend with your replacement owner, it will likely get done no later than Monday mid-day EDT. And it might get done over the weekend; I've just never asked for a midseason replacement on Saturday before.