If it is like my Vermeer 605F, I did as the other poster suggested, sat on the belts to release tension.  I then threw a come-along over the roller that gave the tension, and held the roller up with the come-along.  There was a place, as I recall (been many years since I did this, but I did it a lot) where I could hook the come along on top of the baler, and then loop the cable around the tension roller to hold it.  Using a come-along helps as it is lighter and easier to handle than a chain, plus you can ratchet it up if you need to release more tension.  If you have to remove belts, don't remove all of them without taking a picture of the path, as it is easy to confuse yourself when re-threading belts.  Usually I only removed one at a time, and when putting on new connectors, I attached the new belt end to the old connector, and pulled it through, much easier than threading it.

However, your question was about flipped belts, something that happens often if you don't get the bale started quickly and have uneven feed into the bale chamber.  I often could just fold the belt back in position near a roller, and pull on the other rollers to move the belts.  The belt would often flip back into position without having to remove it.

My baler burned about 1995, which put me out of the custom baling business, our area has lost all but a few cows, resulting in very little hay being put up locally.  If I have something wrong in the above statement, it is because my memory has faded, not a lack of experience.

Added later:  I just re-read you post, and no, there is no adjustment to keep belts from flipping.  My best improvement in baling was buying the Vermeer twinrake, that formed a perfect windrow all the time.  I flipped a lot of belts when starting when using double windrows, guess I couldn't drive perfectly enough to get a large quantity of even hay into the baler at start of a bale.  I didn't flip as many with the twinrake, as each bale would start with an even layer of hay.  There is a lot more problems in baling higher moisture hay than dry with these balers also.  Sometimes wetter hay will accumulate on the scrapers and flip the belts.  If that happens, the scrapers can be adjusted closer to the rollers (not touching them!) so hay does not catch between the scrapers and the rollers.  Sometimes the scrapers will get bent slightly, you may not even notice, from hay catching, and that can also cause belts to slip when hay tries to wrap.  Often, you have less problems during parts of the day than others, as humidity changes.

Don't get discouraged with this baler.  I know nothing about an MF 1560, but if Vermeer makes it for MF on the same blueprints as the 605F, you have a fine machine.  I liked mine better each year I owned it, until a bearing got hot and set a bale on fire on a hot day.  Check those bearings often, and a mounted fire extinguisher is not a bad idea at all!