Ok so it's not actually too difficult.
First, you need a USB (preferably a small one that you don't mind wasting)
Then, put it in ur xbox and turn it on. Go to settings and I believe it's under system you need to find the storage devices screen. Then go on hard drive or memory (whichever one you usually save on) and find the game save for this game under your current account. Select it and copy it to the USB. (The USB may need formatting, just select yes) Then, start a game with your new profile. Any game will do, and you only have to play until it saves at least once. Then find that game save and copy it to a USB. Now comes the tricky part. Take the USB and put it into your computer. You will have to download a program called Modio. Once downloaded, start Modio and click on the M in the top left. Click "explore my device..." Then, in the new window that should have opened, click file and click "open/close drive". The USB should be the only drive to show up, but if it is not then figure out which the USB is. On the left, expand the "Gamesaves/content/profiles" category (under partition). There will be two folders with long, complicated code names. The first will be your current profile, the second will be your new one. Open the second first (with the plus button), and open the gamesave folder you created (It will display game names so it shouldn't be too hard). After this, select the only file in the big section on the right. Right click it and select "Open in register". Then copy the code under "Profile ID". You now need to do the same thing as we just went through to open your gamesave that you want to transfer (it will be under the first coded folder). After opening this one in register, replace the Profile ID with the copied one. Then select "Rehash and Resign". Now this part is VERY IMPORTANT. You have to click "Save to device" and SAVE TO THE SECOND CODED PROFILE. This is your new profile and this will not work unless you do this. Click select, then close Modio and remove the USB. Now go back to the Xbox and put the USB in. Go back to the devices page and open the memory stick. You should now have a gamesave for the game you wanted to transfer in the first place, but with your new profile name under it. Move/Copy (doesnt matter) it to the Hard Drive/Memory Drive that you usally save on, and now when you try to play the game with the new account and select wherever you just moved the gamesave as your drive to load from, it should put you where you left off with your other profile. OH and I should mention, on the Xbox, whenever you are copying a gamesave to the USB or from the USB, you must be logged into the account associated with that gamesave.
The video in the source is a bit outdated for the current version of modio, so it may not be as accurate as my instructions.
Hope this helps you!
Sam