Mad respect to you and your lot! =D
Personally, about half or more of my team sessions (turf, league, salmon, private) are on silent running. Though not due to reasons even close to you and yours. However I have realized a few ideas that could help yall out. And if you're already doing it, keep on doing it!
The biggest thing is to always communicate. In and out of the game itself. Now, you don't have to be too personal, but at least get some idea of what each other is like and how you often play at least on your own. In fact, communication is so important without voice chat that it's probably the underlying theme of this post, always communicate. Whenever possible, communicate. Before a session begins, as you're beginning the session, before a match, after a match, during a breaktime, as a session is ending, after a session. Just communicate whatever, but especially feedback and ideas. Ask for advice, suggest on how someone can improve, and often some sort of accolades when they improved or pulled something off or did something awesome even if it seems unremarkable—like throwing ink at my feet when I'm stuck and can't escape (that always woos praise from me!).
And whenever possible, just play together. And against each other. >=) Do this not just in Private Battles but Turf War too. Over time you'll wind up learning how to keep tabs on one another, how each other plays, how to assist one another, and even how to counter each other—which in turn helps each of you improve, adapt, and anti-counter one another in a beautifully endless cycle of improvement.
Also, develop in-game cues, gestures, and tactics, such as spamming point sensors, using "This Way!" whenever a special is ready for a push, waiting for a partner to respawn when more than one of you has been splatted, long-range inking of areas for your short-range user to move ahead freely and conserve their own ammo, "Ouch" spamming to let warn everyone of a serious threat, and so on! Most of these and more at least one of you will figure out while others will just be made up over time, but none of this will make sense if you don't communicate so everyone knows that "me shooting you in the face is my way of telling you not to go that way."
While you're at it, make use of private battles for more than just fighting. Without all the immediate pressure you can use it to help develop in-game cues that everyone will recognize when they see it. You can learn and plan how to mobilize and maneuver on a map. You can plot and practice things like a Rainmaker run or brella blocking. And you can just goof off to unwind and have background to process past and future matches.
Whew, that's way too much rambling. But let us know how things go and bring back any experience to help the rest of us out too. =)