The slit is the glue joint. Original to the top. Just two pieces joined to make a wider blank. Clean out the joint of all old glue and dirt. Reglue with hyde glue and clamp. Yes remove from the irons first. Hint warm the joint with a hair dryer and then apply hot hyde glue and clamp over night. It will work better if you have lots of clamps clese together for even pressure. This will not hurt the patina. You still may see a small crack but it will be secure. If you separate the two and plane them for regluing you will change the size of the width of the top and the machine may not fit in the cut out.
The original is hyde glue and is water soluble so you can use warm water to soften the glue to clean it off.