"I don't think the Pro In-App Purchase is working correctly"

The "Purchase Upgrade" dialog is designed for exactly that -- to purchase upgrades from the App Store. Some early users got themselves into strange situations, so before allowing you to make a purchase, Composer requires you to Restore Purchases first. This is to ensure that you do not try to purchase something you already have. (Presumably the App Store prevents you from doing this, but I can't control the App Store and have learned that Apple still needs to iron out some bugs in the handling of In-App Purchases.... so extra precaution seems wise).

The easiest way to verify that you have Pro Functionality is to check and see if the Pro Preference pane is present in the Preferences dialog.

If you are truly having trouble with In-App Purchases, you can send me the receipt file from inside the application bundle and I can verify it on my computer. It is located here (assuming you have Composer in the /Applications folder):

/Applications/MultiMarkdown Composer.app/Contents/_MASReceipt/receipt