It's worth noting Beak that there were at least two different types of carriages for the SG1, specifically pre- and post-1961 models. I don't know if those differences included any internal differences that would affect how they mate to the main body (I should try swapping my carriages around to find out), but I would specify the year of your machine in your request just to be safe. 

The easiest way to tell in your case would be to look at the master tab clear levers on either end of the carriage. If they are chrome handles with plastic knobs that stick out it's a first generation carriage. If the levers are completely plastic and look like the paddles on a pin ball machine you have a second generation carriage. 

Well, this thread has made me curious, so I'm going to try swapping first and second gen carriages on both pre and post machines to see if there are any issues. I hope you find what you're after, but my guess would be that it would be easier just to buy another SG1 with the smaller carriage (and it would probably cost the same too!).