Existing members pay double when switching to annual membership

I have just recently added the option of annual pledge and got some members attracted to it. The problem is with my charge up front, they have already paid for September, but when they want to change to the annual pledge, they still have to pay for a full 12 months that will be renewed in Oct 2021. This would mean that they will pay double for September.

I know that refund is always an option, but it will be quite troublesome for both parties when the whole annual pledge campaign was to avoid hassle in the first place.

Is there a way so that my existing members could get a more fair price when they switch? Thanks.