If there are any decent C options for a 16", they are limited. I want to say that my E rated Goodyear Duratracs were sightly more comfortable than current Cooper Discoverer STMax. However, neither are uncomfortable, especially with an appropriate PSI and decent shocks.
There are not any good 285/75/16 tires in load C, most are load E which is the size and type of tire I run (MT MTZ P3). It is a heavy tire that does not have a ton of sidewall flex, I air down to around a 12 psi on the trails. I've never had a load C tire to compare it to but do not doubt a load C would absorb more of the road imperfections. Love the look of them with the MOAB wheels though, a few washers on the steering stops helped prevent rubbing until I got my Antirock.
I have been searching for some that match the same criteria. I have yet to find any in a C rating. However, the General Grabber AT2 has a 285/75/16 with a load rating of D. From what I've read they seem to have pretty good reviews.
I have 285/75R16 Duratrac's. Even though they are E rated they ride very smooth. Although if I had it to do over again I would buy some 15" wheels. If your Moabs are in good shape you could easily sell them.
I did a quick search for 285/75R16 tires (metric 33's) and only found one with a C load rating, the Toyo Open County C/T which does not look like a good choice for a jeep.
I found 6 D load rated tires in that size: the Pirelli Scorpion, Maxxis Bighorn, Nitto Terra Grappler, Pro Comp Xtreme M/T 2, Interco Irok ND and Interco SSR.
One of the reasons there are so few C and D load rated choices in the 285/75R16 size is that this is one of the most common sizes for 1/2 and 3/4 ton pickups that require an E load rated tire in order to support the load these vehicles are designed to carry. Consequently, there are at least 67 E load rated choices in the LT285/75R16 size.
Although some are quick to opine that C load rated tires are the only "proper" choice for a TJ and urge you to buy a new set of 15" rims and go to 15" tires so that you can find a decent selection C load rated offroad tires, my observations over the past several years have been that the selection of 15" offroad tires is diminishing, the selection of 16" offroad tires has remained static, while the selection of 17" offroad tires is increasing. That is why I often say "17's are the new 15's," which is not surprising since TJ's with 15" and 16" wheels have been out of production for 13 years with the subsequent JK's and JL's and many pickup trucks now being equipped with OEM 17" wheels. Tire and wheel manufacturers go where the money is, and that isn't the 15" rim size. If you are going to consider new wheels, you would probably be better advised to go larger rather than smaller. There are a handful of C load rated 33" tires in the 17" rim size and many good choices for D load range 33x17 offroad tires.
The Maxxis Bighorns are a load range D. I have run a set of these completely bald on my Jeep in 255x85r16 size. They don't look terribly fancy, but they have served me well for 40k miles. Not bad mileage for MT tire, really.
Like others have mentioned, I'm switching to a 15" wheel for my next set. Lighter, less expensive tires, with a better variety. Going with inexpensive wheels, you can practically get wheels and tires in 15" for the price of just 16" tires.
I am using a Maxxis Bighorn MT-762 255/85R16-D as a "donut" spare (33.3" diameter x 10.3 section width). Although my intention is that my spare will never touch the ground before it has to be replaced due to age, I think this is an underrated affordable MT tire that doesn't get the respect it deserves. It is on my list to consider at my next tire replacement (along with Milestar Patagonias, Cooper STT/Pros, and the other "usual suspects" such as BFG and GY).
I had forgotten that there is also a Maxxis Bighorn MT-762 LT305/70R16-D, also a "metric 33", that measures 33x12.4". This may be the perfect alternative to OP's desired 285/75R16 size because it is a true 33" tire that is only slightly wider than a 285/75R16 and doesn't have Jerry's dreaded E load rating. Not only is it affordable, OP won't need to purchase new wheels.