I was going to mention as snrub and esshup did, that renovating the whole thing would be the best since it is only 5' deep. Going thru the clay bottom and digging it deeper is really the same thing/question. Like snrub mentioned, it really is about what type of soil you have all the way down to what would be the finished depth. Some areas of the country are lucky with their soil types for this, others are not and there has to be a liner packed after being dug. You say that water is at 4' down, so it might be that if you went past the current pond bottom, the whole water level may drop to that level as a norm. What does your excavator guy say? If he has done enough pond in your area, he may have enough knowledge about this to guide you.
Not having fish in there is probably a sign that it is to shallow to keep fish over winters, especially as they get bigger. That is one reason I would highly consider just digging some portion of the pond deeper. Make use of the guy while he is there. Kind of a compromise between doing nothing and going all the way with it. It would let you see if you lose all the water, and if not, would give a spot for some of the fish to survive the winter. You might open up a big headache tho, needing to fix it next summer if it doesn't work out. It's a gamble either way. Having been thru it myself, renovating an existing pond is more difficult than building a new one.
He might be able to pack a small area, but I doubt that consistently packing a larger area would be very cost effective.
I've seen sheepsfoot rollers that can be pulled by a dozer, but you are correct, it all depends on the slope and the traction that is available.
I have also seen sheepsfoot rollers that attach to the excavator where the bucket goes. Pretty neat...
