I have QuickVoice installed on an iPhone 6 and I had the same problem - that for bigger files it asked for QuickVoice Pro, which even after I installed it, it worked with a new database (being a new app installed), and the old recordings remaining trapped in the free (non-Pro) QuickVoice app.
Here's my fix on it:
When you are in the QuickVoice app and click on a recording (that's longer than 5 minutes) to export it, you will receive a pop-up saying that you cannot send them via e-mail because they are longer than 5 mins and you need to get the Pro version. Hit ok, and in the back you will have the iPhone's sharing options, without the embedded iOS email app (wihch QuickVoice disabled).
You still have other sharing methods available though! - like airdrop (as nloewen19 said above), so you can use that. Another sharing option I used is the Gmail app from Google. If you install the Gmail app and configure your email account in the app, then it will automatically add itself as a sharing option for the iPhone. Consequently, go to the QuickVoice app after installing and configuring the Gmail app for iPhone and you will also have Gmail as an option to send your recording with (since again, QuickVoice only disabled the traditional embedded iOS email app). This method worked for me, apart from the airdrop method above.
You can also use the Dropbox app for iPhone. After downloading the app and configuring it with your Dropbox account, go to the QuickVoice app and hit share/export recording and you will also have the option to save your recording to Dropbox from Quickvoice. This didn't work for Google Drive or Box, however.
Good luck!