What coins are you using right now? The silver Washingtin quarters and Ben Franklin halves will alway be a bit more difficult and wobble at just about every step because of their difference in thickness.
The folding  is a tricky part in the making of the ring but it actually is not that critical of an issue I have found. If it is a little off, it will get straightened out in the reduction steps. The ring stretcher will actually deform the ring quite a bit and make it out of round as well. So it starts wonky no matter what. The reduction dies are the tools best for keeping things true. Here are the steps and some tricks I use:
– punch a hole
– deburr/bevel the hole on both sides
– add a dry lube to the edge of the coin that will make contact with the 17 degree die. I like the dry lube Burr Life but an Ivory soap bar works as well.
– wipe the inside of the die clean of any dust or debris
– set the coin in the die and press the ram down on to the coin to level it in the 17 degree die ( I like to fold with my 1 ton arbor press, gives me more room)
– carefully set the steel starter cone in the hole and pressdown until heavy resistance is felt
– check the hole for any small tears (stress risers)
– anneal the coin. dull red in a dark room. Let cool to a dark heat and then quench in cool water
– place the coin in the 17 degree die.
– add dry lube to my plastic folding mandrel. This keeps the coin from sticking and reduces friction. I like to use Burr Life but an Ivory soap bar works too.
– insert the mandrel and slowly press down. If the coin shifts, I hold the high edge of the coin with one finger and press back and forth from the coin to the ram to level it out. Once close to level, I press slowly and watch carefully. If it is just a little off, I do not worry about it. Press all the way down to where the mandel is making contact with the coin.
– Check for any stress risers
– anneal
– stretch out past my target size. 2-3 for halves, 3-4 for silver dollars
– anneal
– reduce the reed side first to my target size using 17 degree dies first and finishing with 25 degree die.
– roll the cut edge over, using 17 or 25 die, to match the look of the reed side. This side will always be bigger because it is thinner.