The only thing I can think of is creating a collection basin that will catch run off from your elephant pond and from which the water can be then filtered and pumped into a slew that will flow into your elephant pond thereby generating a current that will flood the elephand pond and cause the water to flow downhill into the collection basin. Because you have elephants you could actually fence off the collection basin and the slew areas so they cannot get into them and destroy them.
To increase the filtration on the downflow into the collection basis you could build a wide and shallow area the water will drain into before reaching the collection basin and in which you plant aquatic plants, such as water hyacinths, Pistia, water cress, cattails, or whatever is native to your area that would make a carpet across the surface of the shallow swamp area. Again this area has to be fenced off from the elephants. Because these plants can do a very effective job of purifing water they should grow quite well and could be used as food for the animals, if edible for them, or incorporated into compost.

Here is a link that might be useful: Water hyacinths in sewage treatment

The collection basin and plant filter is probably the best idea. Putting baking soda in it will up the Ph and stabilize it. You need to figure out how much water you have. My 1100 gallon pond takes 1 lb of baking soda twice a year to keep it buffered properly. You could consider getting a fountain that is on all the time to circulate and aerate the water. You will have to ele proof the fountain though. I would think your little pets will eat any plants you put in there or at least use them as toys.

How cool to work with elephants. That is an amazing job!!

I agree with terrestrial man's suggestion. There is nothing like the roots of Water Hyacinth, water cress, etc to filter out wastes and use up nutrients which is what the algea feeds on. I have something similar on a much smaller scale that works well.

I would also imagine the elephants might like the moving water this type of system would generate.

You might contact other organizations that have elephants and ask them what they do. For example try the San Diego wild animal park. I'm sure they have a big pool for theirs.

Their zoo has a hippo pool that is huge and full of feces as they poop constantly in it but it is also full of fish and really clear. I believe they are fish native to Africa that eat hippo waste but you can still see it in the water. It must have filtration too.

I know most zoos have concrete lined pools but I don't think wildlife parks do.

Any plants would help but the elephants would surely eat them.

Partial water changes daily would be a big help but whatever you use will have to filter through something. The slew or bog might not be enough unless it is very, very large and the water will have to be pumped to it in any case.

The smell must be awful!! I don't even want to think about contact with the water. I hope you have good health plans.