Polishing the interior surface of a non-round polycrystalline diamond

Q. Our company routinely polishes the interior surface of a polycrystalline diamond form. When this interior profile is round (or more accurately similar to an hourglass) it is quite simple as we can move the piece in a circular motion as well as up and down. Diamond powder is used in conjunction with an ultrasonic drilling process to achieve mirror finish. However, when the interior profile is square or rectangular, we can no longer spin the piece in the desired circular fashion as the drill needle must take the same shape as the profile. Looking for cost effective ways to polish this interior surface in non-round shapes. Note that the inside of the piece is small 0.250" approx. so this does restrict processing options.