It's my impression that Supreme Court justices write their opinions however the hell they want... as a practical matter if the votes were going the other way he probably would have written a "dissenting concurrence" rather than a "concurring dissent".

Sometimes. The reason he voted against is because he's so aggressively trying to rearchitect the past several decades of 4th amendment jurisprudence that the defendant would have needed to include a very different set of arguments to meet his standards. Gorsuch states that there's a good chance these records are "papers" that the defendant has at least some property interest in, but that the defendant failed to properly raise this argument and therefore waved it by default (so Gorsuch must decide against). He then basically ends with a plea for future defendants to include a set of arguments based on his preferred property-centric regime so he can decide in their favor.