How often do you experience more than 1 tire destroyed at a time? I am assuming you are not riding the tires until the threads are showing and then you ride on gravel. I am also assuming by catastrophic you mean you have no way to repair the tire, i.e. use the dollar bill as Aggie suggests (I have done that too and continued for an additional 1,400 miles), wrap duct tape around it , etc. I have never, in 40 years of touring, experienced a catastrophic tire failure (unable to use anymore), so I am a little at a loss in that experience. Probably just jinx it now.
Honestly, I would like to know how/why you are getting more than 1 tire failure, again you are not riding on sharp gravel frequently. Did you hit a massive hole? The tire itself was a piece of junk? A blowout? Was it on the sidewall, the tread, etc.?
Anyway, if you have never had more than 1 at a time, I would probably just carry one spare tire AND also know the source of where I can call have have another 24" tire shipped to me. This could be a friend, shop, Amazon, etc.
My thinking is say you only get 1 failure at a time. Say it takes a week to ship the 4th tire to you (remember, start with two on the trike and one spare). What are the chances you will have another tire failure within the week you are do not have a spare with you?