First, I love the concept. I had a similar idea (
https://www.dakkadakka.com/dakkaforum/posts/list/810956.page and I'd really appreciate your input), but you went 300% in on it. I identified the same weaknesses and added some hard counters to my list by mostly reducing squad sizes.
I love the captain redeploy shennanigans with this list. But infiltrating units take turns deploying, right? So if your opponent has any infiltrators, they'll have a chance to deploy at least one squad before you can basically zone out the rest of the midfield. You don't need all your squads to be max sized. I'd make the 3rd sniper squad smaller, & save points for more deep strikers or outflankers.
I agree that dropping the Vindicare is the right move. Between that and a smaller 3rd scout squad, you've got yourself 155 points. Get some more deep strikers/outflankers/scorers. I think this list could really use a healthy deep strike/outflank component, to punish an opponent who doesn't screen well or splits up his forces.
Let's talk about each of your identified weak points:
b) 3" deep strike. I'd recommend breaking up the infiltrators into two 5-man squads, to help against the 3-inch deepstrike. They'll cover a lot more ground that way, and one unit can hide behind cover. If you're facing knights/indirect fire, those 5 extra bodies in the big squad won't be missed much in that matchup.
a) Big tough things. A custodes/knights player doesn't have infiltrators, or particularly snipable characters. Custodes'
Dmg-1 on your oath target will make you sad, and might make it worth your while to switch targets once he uses the -1D strat. I think against this player, you deploy your damage doers far from objectives and plink. He can't leave the objectives to come after you, so you aim to score max points on secondaries like investigate signals and move onto just 1-2 objectives he'll have trouble reaching, occasionally diving in with your interceptors to contest objectives. He's going to crush you in melee on his turn even if you send in something twice as tough. Ergo, one more reason to split your infiltrator squad. You weren't really worried about the custodes firepower outside of 12" in this matchup anyway.
Similar tactics may work with knights, since they have limited numbers of units. Against both of these opponents, you want multi-damage anti-armor deep strike/outflank. Preferably units cheap enough that you won't mind using them to score instead. Inceptors may be the wrong choice, at D2, though the 3" deepstrike is very useful.
c) Hyper fast armies: yeah, you've got trouble there, but those armies tend to come at a price or be on the fragile side, ducking behind terrain on their way up the table. The whirlwinds will help with that. So will the brick at the center of your army (Bobby G), inviting the foe to give him wide berth.
d) Servo skull soccer. Game plan: Use a squad of infiltrators to kick an objective into the open where your snipers can all see it. Preferably about 15" from another similar objective and have Bobby G stick around about 15" from both. Now your opponent can't get on them without exposing themselves to shooting and assault. That's all I've got for you, sorry. You're right that your army isn't built for that mission.