I have worked with Seth Thomas mantle clocks. Most likely this one has a square hole in it's minute hand. By now you most likely have seen that flipping the hand upside down causes it to point to the 12 when it strikes its bimbam
When setting the time you do have to pause at the hour and half hour for the clock to strike these clocks do not work like a traditional clock where you just set the time and all is well. You must pause at each half hour regardless of what your doing. Never move the hands backward this is a Count wheel movement and can cause the chimes to go out of sync. You always just start the clock and let it run. When winding never let the key snap back in your hand. Just some tips that can help. You need to watch the time and make small adjustments. You can expect for the winding to be one full turn for each day the clock Ran.
The chiming 5 minutes before is a common issue that comes with age, not just turning the clock. Taking it to a clock shop will be a quick fix of the issue. They will also be able to fix the chime rod issue and clean and oil the clock for you.
