I have never measured any pond with a fountain with a 2-3 ft intake draw pipe where it circulated water down to 8-10 ft deep. I would highly question this claim and would like to see unbiased proof / tests and the methods used. Measurements can be collected with a known or unknowing bias to show an end result.
Since your pond has a relatively constant turnover rate due to out flowing water do you have any dissolved oxygen data collected from the 10-13 ft depth in summer? The deep water may or may not have oxygenated water depending on your pond conditions.
Keep in the fore front of your mind that water weighs 8lbs/gal 5 gal = 40 lbs. You are asking a motor to throw this into the air as high as the horsepower can toss it. Watch a fountain work. It throws the water into the air as high as it can then Mr.Gravity takes over and all the force of the water falls straight back down to the surface where downward force splashing occurs. Very little energy is pushed outward toward the pond edges. Compare the energy distribution with a bottom bubbler below. The big aeration benefit to a fountain is it mixes and remixes essentially the same water over and over. This action highly aerates a relatively small areas in the vicinity of the fountain. This is a big benefit if you are having a fish kill due to low oxygen.
Try throwing 5 gallons of water into the air and you will get an idea of how much energy / electricity this will take. That hard work puts lots of stress on the motor. Fountain motors often have short life spans due to the work load and depending on how many hours a day they operate compared to bottom aeration systems. Air is light weight and pumping it deep into the water and releasing it as tiny bubbles moves lots of water cheaply to the surface. At the surface the rising water spreads out across the surface toward the shoreline. Do more good homework to compare the efficiency of fountains vs bottom aeration.
A good website that has cone more good research than most for both fountain and bottom aeration:
http://www.vertexwaterfeatures.com/aeration/vertex-pond-aeration-engineered-for-excellenceAs an example; I will use the vertex membrane diffuser since they have good water flow data. A
1/3 hp compressor with a 4 head diffuser placed at 13ft deep will move very close to 500,000 gallons of water/hour. This water movement spreads rapidly away from the surface boil. Check with the fountain company how much water each of their fountains move an how big of a fountain you will need to move 500K gallons of water/hr to compare to the 1/3 air compressor.
I am very interested why the two fountain companies are discouraging a fountain. The reasons??
Fountains are aesthetic and produce 'relaxing' sounds which some find very beneficial. Be aware of a high electric bill. If money is not an object then do both types. If you want healthy benefits for the overall pond ecology then strongly reconsider the bottom bubbler system.