In order for the rings to sit flush the design has to be completely redone in a way that the head (the ENTIRE HEAD is the halo, holding the stone, with the sticky outty donut at the bottom connected to the ring itself) is above the band of the ring, possibly involving cathedrals or a reworked head that tapers into a point at the bottom. What I posted a link of from Precision Set is about the only way you're going to get a flush fit with a band, OR a Ritani Endless Love style if the entire head is not reworked to make it happen with less of a donut or no donut. So if having it look identical to HW is important just get HW.
what metal would you file down? The head? the halo? IF you file metal down the chance of losing stones increases exponentially.