The best possible scenario is to size as close to the throat that will chamber/function and not really consider groove diameter of the barrel.
Yondering is correct; the bullet should still drop in a fired case. The case needs to expand to release the bullet.
That shouldn't necessarily be confused with fitting the throat or snug chambering.
So long as they fall into a fired case, make them fit the throat.
Absolutely. Sizing larger than groove diameter is a "by guess and by golly" approach. Measure the throat diameter and size .0005"-.001" under that. Measuring throat diameter is as easy as measuring bore/groove diameter.
When you say "hard cast" what exactly do you mean? Are you measuring hardness with a tester? For a big old .45 rifle bullet used in .45-70 and such, a bullet doesn't have to be hard. In fact, better accuracy and performance can likely be had with soft bullets in the 9-12 bhn range- without leading or resorting to powder coating either.