How can I preserve soy sauce eggs?

My favorite restaurant has an appetizer (or banchan) that my friends and I all adore. They're eggs that have been soaked in some kind of soy sauce brine and quartered.

Back when I was just learning how to cook, and regularly made terrible, terrible decisions, I came up with "Osaka eggs," in that restaurant's honor. (I still make terrible decisions, actually, but now with confidence.) My Osaka eggs are boiled for as long as possible in a salty soy sauce broth. Since it takes some time, I usually make a big batch, and occasionally I lose a jar in the back of the fridge, and a month later they've gone lacto on me. Probably safe, but I'm not a fan.

As a result, I've been considering the possibility of canning them. But I don't have a pressure canner. So I looked into hot water bath canning, and... you're only supposed to do that with sugary or acidic preserves. I'm not interested in introducing any more sugar or acid to my eggs.

So, my question comes down to what can I (or must I) do to preserve my Osaka eggs without introducing a bunch of sugar or acid? Use more soy sauce? Could I strain/reduce the braising liquid and have high enough salt content to make the hot water bath safe?

Or, counter-intuitively, should I not heat the soy sauce at all? I know vegetables are preserved, via fermentation, in miso and doenjang. What about soy sauce? Because with the long braising time, my soy sauce brine is pasteurized.... So, could I actually make my eggs last longer by simply leaving the soy sauce uncooked? (And cooking everything else in some lightly salted water, just so we're clear.)

**Here's the basic recipe I multiply for making terrible Osaka eggs so you can see the relative concentration (or lack thereof) of salt.

(...And a warning that you might not want to try these at home, kids. One person thought they were tea eggs, got all excited, and ended up running outside to spit it out. They taste like ...something that should be meat but isn't meat and some people become confused and even distraught by the cognitive dissonance they create. But I love them and want them to last, dang it.)

• 2 cups of water
• 1/2 cup of soy sauce.I like Lee Kum Kee's double-fermented. Sometimes I'll add some dark soy sauce or mushroom-flavored for part of it.
• 1/8 cup fish sauce
• 1 T oyster sauce
• Some kind of spices: cinnamon stick, cardamom pods, star anise, black pepper, fennel, allspice, cloves, coriander.... Whatever makes you happy.
• .....
• A sliced red onion
• A sliced shallot,
• Some rough-chopped garlic, you measure with your heart,
• A hot pepper,
• 7 or 8 dried anchovies, heads and guts removed.

The first block of ingredients go in a pot, preferably of the crock variety. The other stuff goes in a dry saute pan and are accordingly sauted before being added to the pot. If anything's stuck to the saute pan, splash a little more water in to clean it and add that to the pot. Then add a bunch of boiled and peeled eggs, and let it go however long you want. My friends and I will let them go for a full day or three, and the mushy braised vegetables (and anchovies) are a nice bonus topping for rice.