Hi orchemo and welcome to the forum.
There is talk of stock tire being discontinued (and therefore a new one coming out) - but there is already a more street oriented version in existence.
Normal stock front and rear: Bridgestone TW31 and TW34
More street oriented dualsport: Brigestone TW203 and TW204
or Shinko SR428 front and rear
If you have something else; please let us know as you may have the first of a new style tire for the TW.
Member bananachunks has one of the dualsport sets on his as it is his daily driver - and he has taken it on the tough rides including the Rubicon with other members. So how much less capable it will be for you will depend on the actual roads/trails and your ability and what you are willing to put up with. Let us know what tire they are and you will probably get a lot of responses. Again; Welcome. -J-