Looks like to me an excavator would be your best bet for how you are wanting to proceed.
I've went around a pond like that with a backhoe (tractor/loader/backhoe) because that is what I had, but an excavator would be so much better. One problem with a TLB is you can only park sideways to the bank to give any swing to get rid of dirt. Having room to pile the dirt was as much of a problem as the actual digging. With an excavator and 360 degree swing the waste pile can be further away from the machine and bank allowing a larger pile.
I think you will quickly tire of trying to use a compact tractor to dig much. A mechanical front drive would be a must (waste of time trying with a 2wd tractor), but even then unless you can get right down to solid clay for the front wheels to run on, it's use will be very limited because all your weight is transferred to the front (small)wheels when the tractor is pointing down the slope. A very heavy counter weight on the back end of the tractor as well as rear wheel weights or fluid filled rear tires will help. If time was on your side where everything could dry completely out it might be more feasible. But with the size of your siphon, any reasonable rain event will put you right back where you started. So with that in mind, it is down to handling mud.
Where you are going to use the waste on the backside of the pond, you will need time to let the spoils dry. There will be no way to shape that mud till it dries out some. I cleaned out my son's pond and put a lot of the muck on the back side of a very old, steep dam. It is a good use for the spoils, but it was a mucky mess getting it pushed around there with a dozer. I had to wait till it dried considerably before it could be "worked", and even then it was spongy. I'm going back in this fall to do the final level and grass seeding. I mention this, because there is no way I can see that your project is going to be anything other than a two part project. Part one removing material from the pond, then later equipment coming back to do something with the soil once it has dried out a lot.
The least disruptive (to your way of life) is if the guy with the excavator also has a dump truck with the right type of bed (U shaped) to haul nasty, sticky, stuff. Excavator dumps directly into truck, truck hauls to piling area at back side of dam and dumps where a dozer piles it into a pile that will shed water so it will dry over time. Then about 6 months to a year later comes back with a dozer to do something with it on the back side of the dam.
The other option, which will have your yard screwed up for quite a while but might be cheaper, is to have the excavator simply pile the dirt around the pond, being careful to leave places for water to get around the pile back into the pond. Let it dry in this "windrow" until it is dry enough for a dozer (or loader and truck) to transfer it to the back side of the dam and shape it as desired.
Muck is nasty stuff to deal with. I've cleaned out three ponds so far (I'm no professional, just a dirt farmer with some construction equipment we use around the farm) and it is no fun. I'm semi-retired so I "play" with the Tonka toys while the younger generation goes out and makes a living doing the farm work. Building a new pond is a lot more fun than cleaning out an old one (I along with employees have built 3 new ones). But with your pond location adjacent to your house, you obviously are stuck with the clean out option.
Keep us up to date with pictures as you progress.
Here is a link to my experience cleaning out a 50 year old pond that appeared to be completely dry because the dam had been breached for a number of years.
Cleaning out my son's pond I never made a complete thread about the clean out and expansion of my daughters pond, but here are some pictures and discussion about it.
Daughters opnd expansion and clean out of old portion My two projects above might give you some ideas. Or thought process to avoid some bad ideas.
