Do stratospheric business and military jets use the North Atlantic Tracks?
The tropopause is in the low to mid 30s in the mid-north latitudes that the NATs reside (and is in the 20s in the arctic in winter) so an airliner crossing on a NAT at 55 DegN at FL370 will be well into in the stratosphere.

Concorde didn't use the NATs simply because the NATs top out at FL410.  And in any case, the NATs are a large band of parallel tracks several hundred miles wide which are mostly just shifted more northerly or more southerly to accommodate weather patterns and the locations of polar jets etc.  The routings aren't really customized much more than that.

Anyway, because they top out at 410, if your jet can cruise above 410, like a Global or Gulfsteam, you can avoid the NATs and can pretty much file for whatever custom routing suits you that doesn't conflict with someone else.