A dog would typically have backlash in the faceplate slot.
Are you thinking of a spur center? They are normally tapered to fit in wood lathe headstock bore and need a feeding type tailstock to apply pressure.
A short piece of aluminum round stock screwed to blank should be sturdy. same as you have now but non-crushing, Can't think of any other way using 3jaw chuck.
Spur center kit ,but don't think its what you mean? Does look like this has an round adaptor that could be chucked if you have feeding tailstock, it may work?http://www.pennstateind.com/store/LCENTSET.html
EDIT: maybe a screw type center? extra holes too! (still not designed for 3 jaw chuck but may work)http://www.pennstateind.com/store/CF3SC.html