I built a Dime rig a while back using exactly what he used. RG100HT(rackmount) but the RG100ES is the same but is a head version, Furman PQ4, vintage (blue) mxr 6 band<--only this one. No other eq does what this one does. Its a whole other beast , mxr flanger/doubler, and the rocktron guitar silencer. I even bought 2 Century 200 heads and used those as well.
Thing you have to realize is that he mutitracked on ALL of his recordings to beef up the sound. Live he used as many as 5 heads at the same time to get the stereo effect. On CFH he used 3 RG100HTs as well as the eqs and flanger/doubler.
The mark III does have a similarity in the crunch and chainsaw type aggressiveness he got out of the Randalls.
I would suggest if you are dead set on using the mark III to invest in the mxr 6 band (it must be the blue one that takes batteries only. Do NOT get a 10 band.) and put it up front right after your guitar. The one that says just "graphic equalizer" under the sliders is the exact one he used with the sliders set in the frown shape but not pushed up all the way to the top but just under. Alot of people think he scooped the mids, but he didnt, he boosted them before the amp and leveled them out on the amp matching the treble and mids to about the "4" position. That is a VERY noisy pedal and squeals like a banshee and has frequencies that will make your ears hurt after long periods of play time. Think of the Pantera video where they mentioned "THreeeeeeeeeeee" after they were done playing. Thats spot on. This pedal adds the distinct "fizz" that you hear on the tailend of his tone and adds bite.
After the MXR, put the Furman PQ4 in the chain. I have all his settings if you need them. This helps tame the mxr 6 band as well as beefs up the bottom end and levels out the mids that are boosted with the mxr without taking out the chunk that it provides.
Most importantly and I cant stress this enough, the noise gate to tame the squealing of the mxr 6 band. I prefer the ISP Decimator over the Rocktron as it is more efficient after the Furman.
So, guitar>mxr 6 band>furman pq4> noise gate> amp
The MXR flanger/doubler is put in the loop. This is a VERY important piece of gear that Dime always had, even in the Damageplan days when he switched to Krank. It will help thicken up the tone and give you the effect of two guitars. The bucket brigade delay chip that is used in these is highly sought after and is the key to this type of delay. No other delay produced today can replicate it. Its also great for turn up the dealy and giving it a chorusy type sound like what you would hear on the "Intro" as heard on the CFH demos. The flanger is also to die for. Best flanger I have ever heard.
The pickups play a big part as well. On CFH he used Bill Lawrence L500L and later switched to a hotter version, the L500XL. Later using the Dimebucker which alot of people dont like but when the height is adjusted properly, its mean as hell. Very picky pup that one is on the height.
Thats basically it. This is a VERY high gain setup and when dialed in right is the most brutal chainsaw tone ever. I would suggest running this in full stack form as it adds the fullness to the sound.
On the other hand, if you want to skip all that and go straight for the throat with a plug and play amp to get his tone get the Randall X2. Its basically Dime and Rex in a box. I would also highly suggest trying out a Madison Prophecy. They seem to have recreated the Dime tone with that. You will be very surprised with how accurate they got it. Dean guitars has also, with the help of his longtime tech Grady Champion, created a solid state amp to recreate his tone that will be ready for shipment soon. Something to check out.
Again, if you are stuck on using the Mark III, get the eqs, F/D, and the gate I mentioned and it will get you in the ballpark. It wont be exact because the mark is tube but it will definitely be in the right direction.