Hi Jason -- sorry I'm late getting in on this.
First of all, even though you've progressed past this already, for future use you might want to note that on the Wilton site (www.wilton.com
of course) you can find the standard cake-cutting diagrams for all sizes and shapes of cakes you might ever want to make. (The only thing you'll need to figure out for yourself is the difference in size of the final slice if you veer away from a standard height.) BTW, while there are any number of things that are cheesy on the Wilton site, overall their guidelines are sound and their tools good quality (their pans are truly excellent).
As for the heating core -- sorry you had such a negative first experience. Your comments puzzle me since I have used my core on several large cakes and found it very satisfactory. Can you tell me: is yours a thin aluminum affair, looking very much like a road cone? Is it a Wilton product?
Mine is as I describe above and it makes a very neat little cake "plug" which pops back into the cake nicely, albeit slightly smaller than the surrounding hole. Is there any possibility that your cake shrunk away from the core for some reason? That the gap is large enough that the plug would just fall out the bottom makes zero sense to me ... can you explain?
Best of luck on all the rest -- it sounds grand!