About the only thing I can think of is finding a way to separate them by contact, then save them as text files. You could then copy them into MemoPad, or one of the other notepad apps. That would keep them on the BlackBerry, although they would be outside of the SMS app.
And I konw there is some tool to transfer SMS from BlackBerry to iPhone. Maybe it will take less time to complete this task.
You can back them up to a GMail account from your BlackBerry via a program like DexRex, but getting them into the iPhone is not going to happen. You can transfer text messages from an old BlackBerry to a new BlackBerry via BB Desktop Manager. You can transfer text messages from an old iPhone to a new iPhone via iCloud backups. But cross-platform sms transfer need some third software for the transfer directly.