Jesse,

With regard to salt I should probably rephrase what earlier said. Salt affects the ability of plant roots to take up water. Where you might incorporate such in your soil the salt will be mostly retained within the liner you would construct with it. Think 6" of salt treated soil where the salt changes soil properties through chemistry. The tree roots will not likely penetrate the layer very deeply but grow where the environment is more conducive to their function. Soil chemistry is the key and you should test to see if your soil will respond to this treatment before implementing.

In re-reading, you have several months of continuous water at 24,000 gallons and so their is plenty of water to overflow the pond. In fact far more than its volume and evaporation. If you are worried about a liner's sodium treatment on your trees ... just keep in mind that once the pond is overflowing the trees will get their water there where the soil isn't treated. Overflow can have its own set of problems like erosion for example. So monitor the overflow to be sure the running water isn't damaging you land. Ideally it would disappear into the soil not very far from where it exits the pond. If it doesn't you might want to make some arrangement to help it to do this. Erosion from overflow could be a problem regardless of how you stop the leak as overflow is (not) avoidable in a pond that holds water. If your pond is located over natural drainage (funnels water already) ... erosion isn't the problem but retaining the irrigation on your own property might be a problem for you..

For salt at the maximum recommended rate of 33 lbs/100 feet, you need 1200 lbs or a little less than $350. But you will have to incorporate into the soil by tilling. You should try to compact the best you can to prevent flow through which would leach your treatment. There are hand held compactors that are kind of like a jack hammer if you don't feel comfortable getting heavier equipment into the pond. This isn't what I really mean by compaction but what you wouldn't want to do is fill the pond while the pond soil has the consistency of freshly tilled garden. It is generally not recommended to compact this type of liner with sheepsfoot but to rather use wheeled compactors.

So many decisions. The easiest path is poly-acrylamide like what TJ markets. The only drawback I can see with that is the unknown of how much the trees are taking. PAM isn't going to inhibit access to the water by your trees so this might be worth considering. On the other hand, if you can determine that it isn't the trees but filtration then it would get you on path rather quickly and with much less effort.