Extremely timely discussion! I have been working on the same problem. I have a few ideas (wild schemes?) to share but they aren't tested by me yet. Having been around docks a lot (lived on a sailboat for almost 9 years), both floating-teathered as well as floating with pilings and various variations I decided nothing I have seen to date is a good match for my desires regarding a tea room/gazebo out in the middle of one of my largest ponds. I too discarded the pile drive approach as too expensive. There are various approaches that appeal to me and depending on how soft and how deep the soft goes someone might like one of these ideas.
First, please note that you may pour concrete underwater with great success. In fact I have seen commercial jobs where the surface of the slab was flooded and kept under two inches of water for quite a period whilel it curred a while. I have seen boat ramps poured in sea water (salty) to the satistfaction of the resident officer in charge of construction (ROIC, an architect and PE) at SUBASE San Diego for the Coast Guard small craft at Ballast Point.
If you want a large footprint to distrubute the loading and slow the rate of any subsidence, build forms to be placed on the bottom of the pond with vertical risers of the diameter of the support columns you want. As a previous poster mentioned, sonotube could be used for that and some of the softest silty bottom could be removed before placing the forms. I am considering using large diameter plastic pipe instead of sonotube. I would split the pipe lengthwise and put it back together with hose clamps or similar and other fixtures as required. This form for a column would be attached to the essentially square form so that it would be free standing. the lower end of the vertical pipe/form must not protrude very far into the volume of the rectangular form.
Let me pause here to mention that I am open ocean SCUBA qualified and working in reduced visibililty of a pond with stirred up mud, allthough not really pleasant, is not an impossible task to accomplish by the "Braille" method. Still I would prefer minimum "bottom time" on this project.
Concrete can be poured down the vertical pipe and it will flow down the pipe into the form below, displacing the water in the form. It is my belief (fond hope) that I can use a length of, say, 1 inch PVC as a handle to a tamper with maybe a 6x6 inch flat on the end at rt angles to the run of the handle. With this tamper I hope to move concrete out from the central vertical pipe form to fill the entire form. When this fails, I go in with a garden rake and other implements of destruction with my hookah rig (to not have to carry a tank on my back) or a snorkel depending on depth and conditions. I am considering filling HD bags with concrete and using them to transport concrete to the rectangular form and pouring the crete into the form. This is a back up contingency if the tamper and or rake ideas crash. Another back up contingency is to use another PVC pipe (not split and put back together) as a chute to direct concrete into the area of the rectangular form not near the central split pipe/form. You don't have to go down with a trowel and finish the crete unless you are way more fastidious than I am.
Of course you put rebar in the rectangular form and bent rebar to connect the horizontal rebar to the vertical rebar in the vertical form. I recommend a pretty stiff mix and to mix it for at least 3500 or better yet 4000 PSI. I struggled with thoughts of placing steel attachment points in the vertical cast column but decided I would add attachments to hold structure after cure rather than complicate things. If I did want embedded bolts or something I would place them in holes drilled along the seam where the vertical form comes apart. Based on previous encounters with Murphy, I would probably find the bolts/attachment hardware to not quite end up where I want/need them but as I am a year away from this project I could decide later to take the time to figure dimensions closer. I still need to chat with an engineer who might give me some insight as to load bearing issues to help me decide how large to make the "feet" on the ends of the columns. Left to my own devices, I would just make them so big they would have to be big enough. The reason for the split PVC vertical form is so it can be reused over and over (sonotube usually can't be although it too can be split waterproofed and reused if not embedded in the "foot".
If I opt for a "big bang" job rather than a form a little pour a little process amenable to mixing small quantities of concrete in my 3PH mounted PTO driven concrete mixer, then I will probably use sonotube or waterproofed cardboard tubes gleaned from a roll products operation (carpet, linoleum, whatever) instead of reusable PVC forms and hire a concrete pumper and redi-mix truck. I can make floats to make hose handling easier and just pump the horizontalforms full by guess and by gosh then fill up the vertical forms. If someone tries this method, be careful regarding the mix. Pumpers are notorious for thining the mix to make it flow easily but adding too much water is a BAD idea. Establish in advance what slump they can pump and that it is satisfactory for your needs then hold their feet to the fire to get that slump. They will ruin an otherwise good job if not watched. This is not an oppinion based on one observation or just my experience.
All of the forgoing assumes that there is little or no strong currents flowing through the pond during this work. In strong current situations yo may have to put a lid on the horizontal forms with holes out toward the periphery.
I will be extremely pleased if anyone notices anything impractical about any of this as I would rather have a difficulty pointed out to me now than have a problem when several yds of crete are involved and a lot of forms are in place.
Patrick