I ran 705's for one tire cycle, including a few adventure rides. They are adequate for that use case, and believe it or not also do okay on grass. As you say, mud is their weak point. They do not shed wet mud very well. They are excellent on pavement, do tolerably well in loose dry dirt, and work just fine on gravel and similar. I think you'll do just fine.
I now exclusively run the E804/805 on my KLR. Just put a fresh set on the day before yesterday, in fact. (No, I don't know why the front and rear tires are different model numbers from Shinko.) I think this tire is one of the best kept secrets for the middle/lightweight adventure crowd, especially for the price. It does just as well on pavement as the 705 as far as I can tell, and is significantly more capable in loose off-road terrain.
If you're sick of the damn cotter pin on the rear axle nut every time you take it off, get yourself one of these:
https://www.autozone.com/trailer-hit...ack/207591_0_0
I got a pack of three at the Autozone Across The Street and they're much more easily removed and infinitely reusable. Cheap enough. I gave away the extras to my other KLR buddies.