I would think that if you were going with 2 bikes, the KLR would be too large for the dirt bike. For that use, I would want something smaller that can be tossed around, yet retain some highway capability. A DR650 would be a good choice on the big side, and a DR350 on the lighter side. Either can be outfitted with extensive racks such as the MMoto rack.
If you go that route, I would stop upgrading the KLR before you get too much deeper into it. You can probably find a fast street bike for what you are about to pay for suspension. A friend of mine just bought a Suzuki RF900 for $1400, but I would recommend something more advanced such as a CBR600 or something.
For the single bike route (I have limited space), I went with an Aprilia Dorsoduro 750, and added racks and a skid plate. It isn't as dirt worthy as the KLR, but it gets me into the woods just fine. It is also quite a bit faster than a KLR, with more than 90hp, so it satisfies my speed needs. I think the Triumph 800XC would fit the bill even better, but cost quite a bit more than I paid.