What am I doing wrong

Should be no problem..I personally don't like using glass cannons, especially Alakazam in this fight. I use Lugia, Ho-oh and Dragonite. The fourth mon usually only has to do a little to finish Machamp off. That's what Espeon does for me.

You could check if Mewtwo would be better with Psychic.

Perhaps you need a new phone. Even with a four-year-old iPad Air, I managed to solo a weather-boosted BP/CC Machamp with two Alakazams (PC/FS and Conf/FS), an Espeon (Conf/FS), a Dragonite (DT/Hu) and two Exeggutors (Conf/Psyc and Conf/Solar), all level 30, and with 20 seconds to spare.

The only other explanation is that you did not dodge at all with your Alakazams and Espeons, resulting in them not surviving long enough to use FS.

Do you have a Gardevoir with Conf/DG?

Everything appears adequately powered.
Might want to lead your team with the Zams, particularly against that moveset. I always lead with two PC/FS Zams and (without dodging quick moves) each can usually fire off a FS before the Champ is able to use its first CC, and they are able to get at least one (or two) more off if I dodge the CCs. In the 2nd and 3rd positions the Champ may already have its CC charged a bit once the Mewtwo faints, so it's possible they might not get their charge moves off in time, or just get surprised by how early the CC comes.
I also never use my mewtwo for Champ raids. Mine also has Shadow Ball (though is only level 30) and every time I tried to solo using it I didn't quite make it. I have more success just using Zams, Espys, and a DT/H Dragonite.

I failed a machamp solo the other day on my first attempt with a similar team. I then went on to replace the 3 alkazams/espeons on my team with a W/HP Gyarados, a DT/O Dragonite, and even a SW/DP Dragonite which were all powered up to CPs over 3000. That team leading off with those three won with 30 seconds left. Sometimes brute CP is the answer, especially if you don't dodge.

If you are timing out with this lineup against a CC Machamp, you are dodging way too much. Dodging causes DPS to plummet. You could probably do it without dodging at all; the extra damage you would take would be made up for by the fact that you would kill the Machamp with 30 seconds to spare.

If anything, dodge ONCE each with the PC/FS 'Zams, and not at all with the other mons. Better yet, TM the 'Zams to confusion, and don't dodge. Unless you are using the 'Zams to dodge quick moves in gym battles, confusion is going to generally be better, especially for raids. PC is more fun and easier to use, but it way underperforms in terms of DPS.