I have 2 different Freak Kits, the barrel back will fit inside of the Pump Handle with plenty of room. I'm not sure about the Dye Barrel backs with Spyder Threads but the ones I have (Cocker Thread) are .991" and the ID of the pump handle is 1.088" so I'd imagine they would work as well.
Hope that helps
Started with a Splatmaster, moved onto a Nelspot 007, then came the Autocockers, then a STERLING Pump, next was a Bob Long defiant then a PM7. As of now I have 4 Sterling Pumps, 2 Phantom for SC and 2 Spyder's plus a bunch of extra parts.