How to make the best use of this Machamp?

There is not such a thing as optimal level to utilize max damage, because this depends on the defender. To answer your question it would be level 40, but that's not the answer that you're looking for.

In general, people look up the breakpoint for quick moves. In this case that would be counter. I've searched the breakpoint level for the quick move "counter" against the most common raid bosses where I would use a Machamp (15 attack IV) for.

Lapras: 31
Snorlax: 37.5
Tyranitar: 36

Included the table for Machamp (attacker) vs Tyranitar (raid boss defender)

Well, if we're talking about the ideal level, then the Machamp definitely has to be completely maxed out to inflict maximum damage.

Here's my take: I also have a perfect Machamp, and it's completely maxed out, too. Does wonders against top-tier defenders like Blissey and Snorlax, and has become a vital asset to my attacking lineup when I do Tyranitar, Snorlax, or Lapras raids. If you want to get the best outcome from your Machamp, make him your next project to work on. Meaning, collect enough stardust and candies that will allow you to max out your Machamp to its fullest potential. If you use the IV calculator, and put in Machamp's stat info, it'll tell you how much stardust you need to get your Machamp from lvl 30 to lvl 39 (or lvl 40 if you want that extra damage output). It's definitely worth the investment, cause you'll be using Machamp a lot! Hope this helped!

Taking it to 36 is optimal for resources if you're mainly using it for Tyranitar raids, as it also reaches Bite's lowest damage breakpoint at 35.5, and Iron Tail reaches it's minimum damage long before that at 32.

Going from 36 to 39 costs 52k dust and 68 candies for +4 HP, +3 damage on your charge move and a 1-3 reduction against Tyranitar's charge move which is a negligible increase.

If you don't have enough Machamps to last you through a Tyranitar raid then I'd rather invest that into another Machamp. You can max out the perfect Machamp eventually, but do it when it makes a difference and when you have the extra resources.

Hope you don't mind me piggy-backing on your question but I also have a 100% Machamp and I was wondering the same thing.

My additional question is whether it's worth TMing from C/CC to C/DP. I have enough charge TMs to give it a go and my personal feeling is that I prefer DP. I've been hesitating, however, because some of my raiding buddies say CC is superior so I was hoping for some expert advice.

In case it matters, I'm interested in using it for both raids & gyms, but mostly the former.

To me, while I can appreciate the answers, they're not that useful. To the OP, higher level = stronger Pokemon. This raid monster chart is only useful if raids is all you do, and if they are to stay the same forever, which some players foolishly believe they will and are spending way too many resources.
You want the strongest? Power it up as high as it'll go, forget this BP stuff.

I would max it out (meaning to L39, the L40 "trick" is bush league) and use it for every gym battle.