There's really no change to your process here. I prefer to tape the butt joints so I can then skim out the bead without interference. This would be true whether the butt joint was near the bead or not.
I don't think of taping in terms of "coats". You have a series of steps that leads to an outcome--specifically a flat surface. This isn't paint, and the thickness of your compound applications should be the minimum necessary to achieve that flat surface, not some number of coats.
I suggest that you picture a cross-section of this situation. It's a bead on one end, which protrudes above the plane of the drywall sheets. You then have this butt joint, which would lay below a straight line between the bead and a point on the wall say 24" away, where the taper will end. Since the butt joint is below that plane, it should be completed first.
Drywall is an art, and unless you're pressed for time, just do one thing at a time, let it dry, then another. You'll have less frustration and use less mud (which should always be a goal--sanding should be only to polish the final surface, not to re-shape anything).