How about posting a picture of your Mog? What model tire do you currently have? Several different tires will work well, as long as they air down well (have flexy slide walls) and are used properly. I've used 14.5 Michelin XS on 11x20 rims on my 1300L37 in large dunes in Libya and Tunisia. They had a mild tread and a very soft carcass and worked very well but are no longer available in sizes for your truck. Conti MPT81's also air down well and there's the tried and true XZL.
Avoid stiff tires with overly-high load capacities (for what a 1300 can carry) like the big 395/85 Michelin XL. Of course, the off road champion, Michelin XM47 works very well in the dunes and in the larger 425 size, provides more floatation and retains the bead very well. You don't need deep tread on them so if you find a cheap, well used (but legal) set, they are worth considering.
As far as winches are concerned, I believe your truck is too heavy for an electric unit. PTO winches are simple and powerful but because Mogs have PTO's designed for driving implements (one direction), many are not able to power out reducing their effectiveness. I suggest a hydraulic unit with at least as much pulling power as the weight of your truck. One thing to consider though, how will you anchor the winch cable in the desert? If you have another vehicle, it's better to just use a kinetic snatch strap. If not, it may be better to do without the additional weight of the the winch and plan to dig instead.
Hope this helps,
Pete