[Next_rim]

Couple things, 4-5 cannons at the third is too much static defense, if drops come you'll have a hard time fending it off. I suggest 1-2 cannons at the most likely point they will attack, not directly at your third (your side of the split on antiga or at the base of the mid cliff on shakuras for example).
You will need either a bunch of void rays or immortals in order to not die to a 12 minute roach max.
You also need some form of aoe at ~13 minutes as that is when roach/hydra comes at you, and you need it (collosus and ht also do very well against infestors which is also popular). You won't be able to start a mothership at 11 mins without dieing as it's 700 gas for a mothership and that's a lot of gas (cloak doesnt help as they can just protect their overseers).

Transitioning into mothership before/as you take a 4th base is usually a good time.
Other than that, a ~9 minute third is a good strategy and you can definately defend it if they try to kill it.

I can't question your competence in protoss play, as you are obviously higher in league and rank, but I do have a 78% pvz winrate since I started using the build and I'm rolling 92% winrate this season, and my highest win was a rank 11 EU master zerg. So I feel like I know what I'm talking about.

Yes, I can get a mothership at 11 mins, even earlier, including 1-3x carriers (timing-dependant), lvl 1 air attack upgrade, a sentry, a phoenix and a voidray (also all production). In fact, if I see a 9:30 min hydra push, i can squeeze a mothership at 10 mins just so i can defend it. Moreoever, I created my build to specifically deal with 9+ min hydra timings (drops included). Carriers do enormous damage to hydra, 3x carriers with micro can handle 18 hydras. I'm not even talking roaches, it's just a mtater of time before those die (although it can get tricky if zerg splits army and does 2-way attack or something).

With slight adjustment, it can handle anything in between 10 and 13 mins. This is why I put 5 cannons at 3rd and 2-4 at natural. 2x cannons will not save me from 80 lings, and carriers are too slow to react. I have mapcontrol only up to min 13, then I'm blind for 2x mins, and when I push at 15 with 4th secured, I usually see 10x gases on 5x bases and zerg ready to spam shit. My way of dealing with it is to make them waste supply on useless shit, like cirruptors. Yes, corruptors can kill protoss air, but they can't kill my expansions, and i use recall to force cost-efficient engagements. And I already have massive upgrade advantage and air presence when they come, which in 9 out of 10 cases gives me enough advantage to clear any number of corruptors, hydra or infestors with only 160-180 supply of stuff. Also, I snipe hatcheries in seconds with that enormous dps, so I usually keep zerg contained on 6x gases while sporting 8x myself.

No, it's ridiculously hard to protect an overseer against a 9 range 1-0 carrier (and I will likely have 3, which is a 1-shot with 1 click). I will also have 1 phoenix and 1 voidray. And no, I will not die to a massive roach push for two reasons - I will have ~120 energy for 1 pro toilet, full energy sentry for pro forcefields, and a massive air presence with pretty solid ground in form of cannons. Even if I lose nexus and cannons, zerg will lose more in unit costs, and likely lose his 3rd on immediate counter-attack (I will focus fire hatchery and recall not to lose carriers to corruptors).

TLDR - 11 min mothership works wonders for me, and I almost never lose to 10-13 min timings. I usually lose very late game (25+ mins) due to inefficient trades, or very early game to very well-executed pre-10 min timings. My moto is to be greedier than greedy zerg, and take massive macro lead in mid game with air upgrade advantage and pro recalls.