Just read your speech out loud one or twice before you go into the room. The words stick in your mind really well and help you to fake like you've got it memorized.
But make sure you DO memorize all quotes and source citations word-for-word.
Alternatively, when I was pressed for time, I memorized my platforms the same way I memorized my extemp speeches. What you do is separate the entire speech into three main points, and then separate each of those main points into three subpoints. Memorize the tags for your main points and subpoints (this is easier than it sounds, since your subpoints typically follow a pattern or storyline.) Your subpoints don't have to be strictly segregated, you don't have to announce them and they don't have to be tagged- they should be used more of marking points for your speech.
In a platform, such a setup gives you about a minute for each of your subpoints. If you want to memorize, that means that you only have a minute's worth of speaking for each subpoint, which can help to break memorization into little pieces. if you don't want to memorize strictly, it's easy to ad-lib a minute at a time, and the bullet pointing keeps you on track. Regardless, only having a minute per subpoint helps to keep your speech on time before you have the ability to time it just perfectly right every time. Just make sure that you DO memorize all direct quotes and source citations word for word, since they are very important.
Grain of salt: I'm a limited prepper at heart and only one of my platforms really ever did well. I don't recommend using these tactics as complete replacement for genuine practice and memorization, but they work really well when you're pressed for time.