Air lifts are quite common in aquatics for the low cost/high volume water movement.

What diameter pipe are you considering using to connect to the "start" of your river?

To use the lift to get water flow through a planted area, the planted area needs to be longer, narrower, and shallower than the "main" river for the best use of plant filtering.

If I recall, you were considering a 30 inch diameter connection pipe between the main pond body and start of the river....If so, consider using a Tee style setup normally used for a pond overflow system...You'll simply use air to reverse everything.

In a 30" pipe, you could create a cluster of several membrane style diffusers to create an astounding amount of water volume being moved. Remember, it is not as important to have air volume as it is the have air surface area, meaning a million tiny bubbles have a vastly larger surface area than one air bubble occupying the exact same volume in water...Membrane diffusers create bubbles measured in micron size. This setup could potentially create 1000's of gallons per minute with only a 4-5 cfm air supply.

The main keys to consider for High volume, low cost water movement is pipe diameter, the longest possible vertical rise of air, and air bubble size. Other less critical considerations are smooth bore versus corrugated pipes, sharp, versus smooth angles, and pipe distance friction loss.

If budget allows, I would suggest pulling water from the deepest point in the main pond pool area. REGARDLESS of budget, use fool proof safety guards on both the inlet and outlet so no swimmer can swim into the pipe for "fun"! (suction really won't be dangerous in and of itself) Use a 10-20% larger diameter inlet supply pipe than the outflow/vertical riser pipe diameter....Have a pro do a site visit to help avoid costly insurance to build right than to repair potential mistake later.