I would say go with a 338 edge, you have the sub 30 cal covered well, and there is not that much of a gain to go 300wsm from what you already have. That said I have a 300wsm, a 300 win mag, 300rum and an edge AI. I couldn't decide either so I have been slowly trying them all. If you want accuracy and ease of wind reading at long range you need to push a bullet with a G1 BC in the mid 0.7 or higher. Reading the wind becomes very important and going to a higher BC makes things easier. The edge also seems to be very easy to load for. Redding dies are available from Sinclair's or Defensive edge.
If you want a single shot start with a used Savage LRPV, it has a decent stock to start with and the target accutrigger. The ejection port is large enough to eject a RUM casing. Switch the bolt heads ($60 from SSS), and try out a shilen or pac-nor pre-fit in 338 edge. If you can handle reloading you could likely switch the barrel yourself, or most smiths where I live would charge 50-60 bucks. All you need is a barrel nut wrench, go / no-go gauges and some patience. Of course you could do the same in a 300wsm, and push the 208gr amax.
The 300wsm is a fine choice, but the 338 class would be a noticeable step up from your current selection of calibers.