I have failed twice myself with the need of one more charge to win Everytime and I just can't do enough damage. My one thought would be does the SoB Eggy work better than the P eggy because I used 2 psychic Eggies and felt like they performed great even though I couldn't get over the hump. I think I am missing a double dark Tar which I just was able to TM and then max(i am lvl 36) so I am excited for another chance. I have also considered using a double dark Houndoom but I have not had the chance.
Gengar with Shadow Ball (Solo Failure #3)
There won't be a 4th! But I need some advice.
I've really wanted to add Gengar to my tier 3 solo success list, but after 3 attempts I have nothing but a bunch of fainted mon and a dwindling potion supply (and yes, dust, the new consolation prize). I have an older phone (Galaxy S5) and rarely get >173-174 seconds. My phone is too slow to start with a second team so survivability is a must.
I came very close with this team (see screen shot), both Gengar and Snorlax had only a sliver of health remaining. I switched the Eggy for the Espeon the game had lined up (same spots) because I found them to be very fragile glass cannons in previous attempts.
Why does every Gengar have shadow ball? Must be abother glitch since the upgrade (just kidding.... anyway, I want to defeat him now, just because!) I have managed Machamp with CC and even DP (plus Scyther and Porygon), but I would really like to add Gengar before I get my new phone.
I dodged a few times to ensure survivability but it may have cost too much time. Any and all suggestions and feedback appreciated!

Answers
SoB is resisted by gengar so if you use eggys you should use psychic ones. Also, snorlax lick has a breakpoint at lvl 27.5 with 15,14 atk so you want to power it up to that. It should give him a significant boost in performance. Do you have any dark houndooms? I would change the eggys to that or DT/O Dnite.
For starters, get rid of Snorlax. You don't need an anchor; you need damage. For instance, evolve, power, and use an Espeon. An enormous upgrade in damage output there.
That change alone should put you over the hump. Also, though it goes down quick, another Gengar with Shadow Ball can get you ahead of the timer. Just don't lead with it so it doesn't have to absorb the first two quick hits.
If survivalability ( and winning off course) than win with fast time is your goal..
My advice is dont use exxeggutor, gengar have SE against grass
Your Tyranitas is good enough, whether you want to change the SE with Crunch is up to you.
If you have atleast a level 30 Alakazam and Espeon with good moveset against Gengar, use it, they are actually very good counter against Gengar.
Gengar is also a very good counter against Gengar but you still dont have it yet, so Zam and Espeon will do..
Dont worry about the shadow ball, it can be dodge quite easy, just wait until the black ball about to launch (getting bigger) then dodge it.
If you manage to dodge it with zam and espeon, and succeded in launch their own charge move twice, you have a good chance of winning it.
Then use your TTar after that you can tank it if you like or do some selective dodge.
Should be enough with those 3 TTar, but if you want and you have it, a MudSlap- Earthquake Rhydon in last position as a tanker is good, way better than Snorlax.
Although it seems like it should be good, the Snorlax doesn't do enough damage even beyond the lick breakpoint. Swap him out with something that does high super-effective DPS, like a double dark Houndoom, or a double ghost Gengar, or another T-tar if you have one. Or, even a DT/O Dragonite would be an improvement.
Solar beam is resisted by Gengar's poison typing, and psychic is super effective (along with being two seconds faster than solar beam), so swap out the Eggys for double psychic ones. That should be enough to get the job done.
Oh, and don't dodge very much. I'd suggest not dodging at all with the T-tars, and no more than once with the Eggys or other glass cannons, if it will allow you to launch one extra one-bar charge move.
I think you need to prioritize higher damage attackers over some of the tankier ones there, at least replacing the Snorlax with something glassier, and probably the first Tyranitar since that one's only doing neutral damage. The Exeggutors too, actually, since Solar Beam is resisted, and they're weak to ghost. It does require a careful balance not to go too far the other direction, though, like what happened to me last night.
I saw a Gengar raid for the first time in like a month yesterday, and it was my last chance to use my pass from the day before, so I decided to make my first solo attempt for one of those. I only had enough time for one try, though, and it had Hex/Shadow Ball. I decided to throw mostly glass cannons at it, since I figured Shadow Ball shouldn't be too hard to dodge, so I used my Mewtwo, 2 Espeons, a Gengar, Bannette, and my one strong Tyranitar with Crunch.
Unfortunately, my Mewtwo managed to get dodge glitched, even though that usually doesn't happen during solo raids, and then everything else but the Tyranitar was going down pretty fast just from getting hit by Hex, plus one or two got hit by undodged Shadow Balls during my own charge attacks. So I had him almost beat with about 28 seconds left, when my last attacker fainted. I never used to be able to rejoin a fight with new attackers, but it's been working lately, so I jumped back in with the autoselected Bite/Stone Edge Tyranitar I left out the first time. I should have had plenty of time to win, but once I got back in, the Gengar had mysteriously healed a significant chunk of damage, so it had about 3x as much health remaining as it did when my 6th attacker fainted, which meant I ran out of time.
I would have won if it hadn't healed, so it seems like going back in with a second round of attackers still isn't an option. So yeah, you should have used fewer tanky fighters, while I should have used one more instead of that Bannette.
I would bet it's your slow phone (cpu & network) cause I have the same problem (Honor 5x), and have failed at gengar with SB 2 out of 3 times. Can do all the other T3's you mention as well on a regular basis.
IMO, the problem is that short charge moves like Crunch take longer for the phone to animate then their duration, so the effective DPS is lower.
Compensate by putting a couple of Espeons/Alakazam with Futuresight up front. But it's still a hit and miss thing - you'll get the FS's in, or not depending on timing. Also, you really have to go hard on your Tyranitars, possible missing a dodge or two.