If you're using R^3 engine offline using Adobe AIR, you can actually already do this as long as the
Auto-Save Replays Locally setting is enabled inside of Other Options.
If that's enabled, then you will have a folder inside of your R^3 root called Replays that you can navigate to.
Inside of there will be some folders that seem to be named with hashes of some sort; these represent the various engines that you have played on. Inside each folder is a list of text documents that actually collect every play you have completed - so long as the setting mentioned has been enabled.
The replay name has some identification mechanisms to help you track the exact play you are looking for.
The digits before the first underscore are the level ID, assuming that the level ID is numeric; this behavior seems to be correct for custom songs too. From what I've observed, if the level ID of the custom song that is played is not numeric, it seems to grab the sequential number of the level in the playlist XML (i.e. if an entry is four children inside the tag that houses all of the data, it will record with an ID of 4).
The digits before the second underscore are the epoch timestamp (in milliseconds). If you have a sense of when you had a session but aren't sure what the level ID of something was, you could
plug your time here, change GMT to local time, click on
Human date to Timestamp and take a look at the timestamp in milliseconds field to assist you in identifying stuff.
Everything after the second underscore is rudimentary and very familiar - it is your performance: perfects-goods-averages-misses-boos-max combo.
Once you have found the replay that you are interested in, open the text document and copy the contents of it, then go back to the engine and press F2 to bring up the Replays menu, and click
Import. Paste the contents of what was previously copied from the text document into this textbox and hit enter.