I forgot to post about this at the time, so this is a bit old now, but nonetheless worth sharing.
As part of MR 801 on copy paste improvements, there is now a new option in the paste special dialog “Assign unique reference designators to pasted symbols”. In addition, this same dialog has been ported over to pcbnew so now copy/paste can be consistent between the two applications.
I personally use the new option as a very rudimentary design reuse feature. If you copy paste the same block in eeschema and in pcbnew using the “assign unique designators” option, the reference designators should generally match up, so you can then link the two up (via “Update PCB from Schematic”) and that will ensure unique nets are assigned and everything generally works.
There may be a few edge cases that aren’t covered: for example if you paste into a sheet that is instantiated multiple times in the schematic, you would essentially need to paste the same block in the pcb the same number of times as that sheet exists in the schematic.