now let me get this stratght, you want to change dies, how about the base plate (shell holder) that is different too. So without knowing which machine you are usiing. If you change dies and base plate I know of no reason you couldn't reload any caliber under those guide lines.
A Dillon "conversion" is the shellplate, retaining buttons, and powder funnel/neck expander. You have to have the shellplate and buttons to match the case rim. You might be able to use the same powder funnel, I don't know if the length is different from .45 ACP to .45 Colt.
I have to use a different shellplate and locator pins when I load 45 auto-rim, so I'm pretty sure you'd need a different shellplate for 45 Colt. Like Jim, I'm not sure about the powder funnel, but I suspect it might work.
I got my first 45 Colt about 9 months ago and borrowed a set of dies from a friend. I think they were RCBS. I was using Winchester brass and 250gr Meister bullets. The brass would not size down enough to get a good grip on the bullets so I decided to try my ACP dies. They worked perfectly. They even produce a respectable crimp. I have been using them to load my 45 Colt ever since with absolutely no problems. My hottest load to date is a Beartooth 330gr wfn moving 1200fps from a 5.5" Ruger Bisley.