Unfortunately your only options for complete elimination of bottle sediment also eliminate the possibility of bottle conditioning. You'd have to filter and force carbonate and then fill off of the keg.
Now, you can greatly reduce sediment through means like cold crashing, or gelatin, or some other way of stripping the yeast out in the fermenter and leaving it behind. The little bit of yeast left in suspesion should still be able to carbonate, and leave a very small tight yeast layer in the bottles, to the point where it can almost be poured in entirety without disturbing it. However, there's a line where so much yeast would get stripped out that you'd no longer be able to carbonate.
There's also the Biere de Champagne method. Can't say I've tried it. Can't say I know of anyone who has.
Point I'm trying to make, bottle sediment is part of bottle conditioned beer. Nothing to be done about it.