A quarter inch rod will probably work. Ram it in, mark it, cut it, then build it up in a couple spots so it doesn't rattle around.

I crammed a 5/16" rod in an old ping 7 iorn, and it's the same weight as the momentus Jr.

Next, I'd take the grip off, use lead tape in place of buildup tape, and put another grip on.

Finally, plaster the head with lead tape, and wrap the shaft in lead tape as well.