You don't want to let it expire and take your chances with moving it. If you want to move to another registrar, go to that registrar and initiate a transfer.
You should be able to transfer without any additional fees. The transfer request adds a year to your domain registration expiration date.
If you let your domain expire - it may not be available for quite some time for registration again, and you may not be the one who gets it back when it does come available. When you let a domain expire, it effectively becomes available only at the whim of the registrar. For some, like OpenSRS, it's a predictable process. For others, no one knows how long it will take.
Is there some reason you've not simply done a transfer?