Widest tyre you can safely fit on 700c wheel (17mm rim width)
There are loads of 2.1" MTB tyres, and a few 2.0. I've got some WTB nano 2.1s that were on my hardtail when I got it, and I've got a Rapid Rob 2.1 on it now. 

But your current tyres look pretty slick. Putting a dirt touring tyre like a marathon mondial on there would certainly help (and that comes in 35, 40, and 50mm widths). Those are OK on road, though slower than I'd choose for all-tarmac use. I take my tourer off road too (though not laden) and have really noticed the difference between the marathon mondials and the slick marathon supremes I switched to (or indeed the marathon plus on my hybrid), even with both at 35mm.

The footnote to the table you link suggests you can go a fair bit wider - in fact my hardtail has narrower rims than my tourer. You're likely to be limited more by the clearance batten the chainstays/seatstays/forks.

The tyres I mention are just examples, based on what I've used.