How to preserve this agar based dish for humans?

If it lasts for 1 or 2 weeks at a time, then I'd suggest making 1 to 2 weeks' worth at a time. Alternatively make the whole batch, but divide into small portions and invest in a vacuum sealer to remove all oxygen before freezing. The vacuum bags provide convenient freezer store as well.

But.... Thing is that just reducing the risk of mold won't stop your highly nutritious human food from decaying in other ways. Once eggs are out of the shell, they don't last long. Something with high water content, honey/sugar, and potential bacteria from the raw egg, not to mention the environment, is going to start fermenting, and agar is straight-up used to make those little culturing plates used in labs. Fermentation will still happen at fridge temperatures, even if it takes longer. Your sludge sounds like a great substrate for nightmares, as you've evidently witnessed on the mold-front, so for the sake of any human interacting with this stuff, I'd honestly recommend preparing smaller portions.

You can do that more easily by blending the egg to really liquify it, then weighing the egg and the other ingredients. Once you know the weights of everything, scaling the recipe is simple, and the liquefied egg is easier to measure.

The egg liquid can be preportioned and frozen (use a silicone ice cube tray if the amount of egg per portion is too tiny. Then just put the egg cubes in a freezer proof bag for long-term storage and hope for the best.) The ingredients can be combined/frozen where appropriate.

Alternatively,you can try powdered eggs, which are reconstituted with water. My concern would be that the drying (or pasteurization) might affect the proteins in a way that these humans like even less, lol.

But as rumtscho said, this food is simply not intended to last. Barring some kind of commercial preservative/mold-inhibitor approach, you're going to have to prepare it differently, prepare less, or decide if it's still cost-effective to make your own with the amount of loss each month.

Very simply: you can't.

The shelf life of food is "built in" into a recipe. If you want something which lasts for a long time, the whole recipe has to be created around it being long-lasting. For example, if you want a piece of meat to last a long time, you have to turn it into salami, or pastrami, or something else that is durable - but you cannot have a piece of meat that does not spoil. Similarly, for your recipe, there is nothing you can do. If you keep it in the fridge, it has a shelf-life of 3-5 days, and after that it is officially unsafe. There is nothing you can do about it.