That's odd. I thought all the Lyman and RCBS dies were interchangeable. Can you put your calipers to the length and OD of the die?
As to the top punch, since a wadcutter has to go all the way into the die, and there is no narrowed ogive for a top punch cavity to surround, using a sub-caliber straight rod with a flat end or doing half the bullet at a time, then turning it over and doing the other half are the only options that occur to me right off. I've never cast lube-groove wadcutters; just tumble lube bullets that I fire as-cast. Perhaps a top punch that starts it in, then has a short straight brass rod substituted for the bullet nose to push it in the rest of the way would work. You'd have to set up the ejection to work with the rod in place.
Even in molds with lube grooves, these days I frequently just use Lee Liquid Alox or White Label Xlox tumble lubing, then use a press with a Lee sizing die on it. These are push-through dies that use a sub-caliber ram mounted in the shell holder and a long taper to straighten the bullet's entry into the narrowest part of the die. After pushing through, you can apply more lube if you wish.