Dry Mud. Different from thick wet Mud
Don't mean to bust your balls either but....Shinko 705 great in dry Mud (just like concrete - pic1 & 2) not much better than a street tire when mud is real slimey or an inch or more thick. If it had been raining a lot more in pic 5, shinko 705 would have had lot more trouble. (Nice dry stretches of mud between little bit of wet mud no count
I ride Shinko 705's on my 1150 GS all the time and I think they are a GREAT tire, I don't do serious mud in them (inch or more thick) I have smaller bikes for that.
The 705 will serve you well over dry gravel (as in pic 4). They'll do well over coarser stuff too.
I think to the OP, my advice is differnet. Don't try and bust your balls on day one with your new Bike. Learn it, feel how it behaves. It'll be different from a KLR, it will likely be a lot less forgiving when needed to brake quickly etc. It takes time and lots of practice to ride a bigger bike like that well and IMHO it is a different skill from handling a smaller bike. (Not that I am an expert at either).
The Shinko 705 is a great compromise for your bike, really good on pavement & dry gravel. If you really want to hit wet gravel and/or mud TKC's will serve you better.