I know that this is difficult for you and I do not envy the position you are in. This is why I have suggested trying to separate them into groups or potentially rehoming some (maybe even temporarily into foster families if a cat rescue could help) to just try to make this a wee bit more manageable for you and give you at least a chance to work on identifying a trigger, settling them, and trying to restore the peace. Because as it is, I feel you are just stuck in a cycle of them being unhappy, reacting, you being unhappy, and unable to address what is settling them off. And it breaks my heart for you because I can tell you have really tried and the kitties are just not giving you a break.
You mentioned that you are concerned about putting the non-sprayers somewhere they do not have access to the garden. But if the garden is being invaded by other neighborhood cats, which undermines your cats' possession of said garden, that could be enough to trigger spraying (as the house spraying would be a reclaiming of the territory as theirs). So, despite it being a 'cat safe' garden, it isn't a territory that is safe from other cats.
So, if we are concerned that this was the trigger, removing access to the garden if there is someone else marking/claiming it, wouldn't actually be a negative. It could potentially remove a trigger and if it is the only one, then we could see cessation of spraying. But mind you that is only as long as (1) the neighbor cats don't start urinating near vents/doors/windows (so the cats inside can smell it and be set off again) and (2) it is the only reason behind the behavior (which sadly there is no rule saying cats can only do things for one reason).
I agree that rehoming would be hard, especially since there are so many cats in need of homes. And while turfing the 'problem kitties' out would be a method in trying to restore people for as many cats as possible (which is us trying to keep as many home with you while tryng to allay the ongoing problem), it isn't a perfect solution. Because even if they are removed from your group, we do have to acknowledge that this is the most common reason cats are rehomed and its a stigma that will make these even harder to home.
Overall, it is without a doubt a difficult situation. One or more of your cats started spraying because of an anxiety trigger (ie other cats in the garden territory, not getting on with a cat in the house, etc). So, he sprayed -- his way to send a message since cats don't do email. Other cats in the house either have the same issue (thus reacting this way too) or potentially are having issues with the fact that cat number one is reacting in the manner. And as it goes on, it can even become a habit (as they get used to this being what they do) and the original meaning can even be lost at that stage.
Furthermore, if the cats are upset about something they cannot control (like an outdoor cat, etc), then they may choose to redirect their aggression. So, this can then lead to the fights you have seen. As well, if the sprayer's work upsets the others, they may then get aggravated and pick a fight over that.
And this leaves us in a middle of this chaos, trying to tease out what has gone wrong and wishing for once our cats spoke English. Your addressing the stress was appropriate but if the triggers are still in place then they will be blocking your progress. Therefore, we still need to try to find the trigger (which may be easier once we know who/how many are reacting) or we have to consider removing the reacting cats from the trigger.
So, do consider CCTV if we can't isolate/monitor due to limited space. Make a list of all the culprits and monitor their interaction with others and the garden. This may give you a clue of what is fundamentally bothering them. If you can find the cause and can remove it, we may see them settle. But if we cannot identify the cause or remove it, then that may be our cue to consider seeing if there is somewhere else for them to calm down and find peace.