This is going to be anecdote time. I keep killies, and many breed best in shallow water. If I were doing such a tank with tetras, I'd think of something like H amandae, Axelrodia riseii or one of the other smaller ones.
First, it is hard to change water when it's shallow. It really affects siphoning, and that leads to waiting til tomorrow. But the water volume is unforgiving - a key reason why water volume does matter.
A shoal of small tetras should be around 8-10 or more, and my personal rule of thumb is no shoals in 10 gallon tanks because of water stability. Tank size is part of it too, A long low tank would be better. But it's still not a lot of water.
My homemade paludarium is 40 with about 20 gallons over 48 inches. I have Chromaphyosemion poliaki killies in there. They don't shoal but are social. Have you considered Epiplatys annulatus?
The tetra I had in mind was
Aphyocharax rathbuni. I understand what you're saying about water stability with a shoal of acceptable size though.
I do have some experience siphoning very shallow water (we have long, shallow sea tables at the marine station), so I'm definitely aware how much of a pain it is, but that's why I have a personal limit on the number of tanks I keep at one time, and that number is only three. It all gets factored into how much time and energy I have for maintenance.
I hadn't considered
E. annulatus, but you're right, they could potentially be a good fit. You mention many killies prefer shallow water for breeding. Are
E. annulatus one of those? Are there any other killies that would be appropriate for ~10gal of water? I might like to try my hand at breeding if a paludarium setup is conducive to that. I know a lot of the annual killies do well in small water volumes, but I have a feeling the frogs (which are semi-aquatic) would eat fry, and it'd be nice to not
have to rely on successful fry rearing in order to enjoy a fish for more than 9-10 months.
Edit: and yes, I know a separate tank is usually used for rearing fry, but in case I can't have a separate fry setup, I'd like to still be able to enjoy the fish for longer than what an annual species can provide in one generation
I've also seen WCMM and medaka in very similar setups with similar volumes of water, so those could also be an option. I've seen some very beautiful medaka varieties and I understand they're a good beginner fish for breeding.