If there are no fish, then draining or drying the pond is by far the best way to perform your renovation.
A long-reach excavator would also work, but they are expensive and if the operator is scooping in water, you have only poor indicators that you are about to break through the clay bottom.
You say the pond is fed by a spring. Does it also get some surface run-off from the waterway that is at about 6:00 on your photo?
If you could divert the water supply from all sources, then you could pump the pond dry and renovate much more efficiently. (However, it will still takes lots of time, since the muck will have to be worked and allowed to dry.)
If you do have good clay soils, then you should be able to deepen the pond to whatever level your budget allows - even if you go through the original seal. Dig about 1-2 feet past your desired final depth and stockpile some good clay in your pond basin. Dig out any sand patches or channels. Then re-seal your pond in 6" lifts of moistened clay.
Then add a fishing dock, swimming platform, fish structure, etc. before you break your water diversion and allow your pond to re-fill.
Good luck on your project!
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