In the one pic , I can't really read the name or tell what tire it is you are currently running ....... Also , what I noticed in the one picture of the knobs tearing , which usually indicates being/riding aggressive on hard surface , such as hard dirt , or hard pavement and being a bit harsh on the throttle as opposed to just "cruising" around .... so knowing the compound and designation (dirt ,D.O.T. etc.) of those tires would help .... A soft compound tire , though great for traction , is easily worn , as well as tears knobs off easily when stressed on any hard environment street or dirt (I have gone thru several tires where I hardly had any physical wear , but the knobs were torn just like yours or torn completely off , this was a result of using the wrong compound tire and riding real aggressively .....
Using a tire that is dirt specific , means it will not hold up under "road" conditions , as well as it is not D.O.T. approved , which means the same thing , it was not intended for that use and also has a lower top speed restriction than a road specific tire (if a cop really wanted to push the issue , he could write you a ticket for using them) , in other words you really want a D.O.T. approved tire , not necessarily needing a street tread pattern , just a tire designed to be ridden on pavement , the difference affects stopping distance , and a lot of other things that I really don't have all the info on , but know enough that one is not the same as the other
What you can do is find a D.O.T. tire that will also work for you when you go off-road , I do not know the percentage of street vs off-road you ride , and that will make a difference in what tire you would want to use , the more street friendly (D.O.T. approved and knobs not tearing etc.) the less dirt friendly the tire will be as far as traction off -road , so you need to consider how much of what riding is more important (unless you get a used set of wheels and swap from street tires , to actual dirt tires , so there is not compromise) , but that is the issue , is there is not really one specific tire that will do all for both street and dirt equally without compromising something , there is always a compromise and only you can make that choice of what you are willing to live with , or live without .....
But my suggestion is if you are only occasionally going to venture on the road , then get a tire that is D.O.T. approved , but barely , this will give you the safety requirements the law wants you to have , and still give you decent (not great or even good) , but decent off-road capability ... or if you are mostly riding the street now , then go with a better street design (which will mean it should last much longer) and live with what you get for off-road ... ... I can't recommend a specific tire or brand , because the variance is dramatic depending on the use specifics as mentioned ....
Hope that helped some .... hopefully someone else who rides the conditions you do , can chime in with a recommendation that is more specific ..... I pretty much stick to the dirt anymore (since the mid 80's) , I feel much safer fighting off the occasional tree in my path , rather than a 6000 lbs vehicle in my path .... I spent a year in a wheelchair because of one of those exact encounters , and do not wish to do so again ...
EDIT: .... It looks like Ray chimed in with some good info while I was writing my 20 page story ........
