I have the same type of winder as you, as it is only the inner tang to catch the spring you need to worry about cant you just turn the spring over and wind it in reverse? It should just push out into the barrel.
Or if you wind the spring into the winder, it then is the wrong way round to go into the barrel? If this is the case then it would be a matter of making a sleeve that is the same diameter as the winding barrel, push the spring once wound into the sleeve and then from the sleeve into the watch barrel. I hope that makes sense?