I did it! A big thanks to the Gamepress community!
After 3 failures over the last month and a half, I finally soloed Machamp today (see team pictures below)! I definitely got off "easy" since he had BP/CC. But I know I wouldn't have had a shot without all the experiences and advanced players who frequent this site. You all have been extremely helpful in my Pokemon Go journey and I try to give back by giving my input. But to anyone who has every given tips and advice on this site, thank you!
As far as the battle goes, I was generally lucky. I only had one mon switch straight into a close combat. Most of my team got off multiple charge moves before fainting. I only dodged a couple times, but they were generally well timed.
To to it all off, I caught the boss first throw with a pinap berry! It was a good day for Pokemon!
P.S. Pictures below.

Answers
what is the best anchor for Machamp ?
ive just been using my C/P exegg as one in my teams currently.
I tried a Gyarados once..and he seemed good in terms of his bulk/how long he lasted. He could take 2 or so charge moves without dodging.
But the dmg seemed to be alittle too lacking for the time limit I was against so decided not to use him
SoB sims as well as Psy in this setting and in my opinion on the more predictable charge moves is actually better.
But I've only used DT/H Dragons. He does much better damage while surviving with an SE hurricane charge. If you really kill it with your front end DOS guys a Lugia with Es/SA should clean up well but this is a greater investment for most from a versatility/candy standpoint. I don't know of any other anchors worth getting in to.
Good job, it feels good to finally solo a tier 3 doesnt it.
I actually finally solo'd a Machamp yesterday too.
I definitely seem to do better vs heavy slam.
But it could just be crappy lag situations while facing him with his other charge moves.
My team was also the same as your except for a Dragonite in place of the 2nd Exegg. I am trying to get a 2nd one with good IV's and SB.
Its been more than possible for me to do it for a long time...its just the terrible lag and stuff that has made me fail...just overall messy laggy fights, taking insta charge moves as my pokemon come in etc,
I need to dodge charge moves to have a chance, I have gotten so close previously...his hp bar has been barely visible when i time out, where I could safely say, just dodging ONE more of his charge moves woulda let me do enough dmg to have beaten him.
But no warning/flash when the charge move is coming...combined with literal spam (sometimes just constant back to back charge moves) and tons of lag...its just so inconsistent. It feels luck is a big factor in finally getting a 'good run' and beating him.