I have to agree with Lisa here. I understand it might be tough to find someone to do this for you. However if he does not have experience moving large boulders I would be hesitant, I assume he is charging you on an hourly basis so you do not want to be paying for his education, lol. Your site is very tricky with the slope. I can attest, using my kubota, that slopes are tough, plenty of videos out there of tractors rolling over, almost always because of not being careful on a slope. Most of those videos you see moving boulders for pond builds are on fairly flat areas, if there are slopes then they are using very large excavators with large booms. I could be wrong of course, not knowing the exact layout of where the excavator would be and where the boulders would be moved from.
Using just the bucket would not be an option (or should not be). The boulders can too easily fall from the bucket and its thumb. Using a backhoe to remove stones from the ground is fairly easy (believe me I know from all the stones I removed) because you are not concerned about where you are putting them, you are just trying to grab them and manipulate them so you can get them out of your excavation area. Trying to place a boulder with just the bucket would be too difficult because once you roll the bucket to release the stone it wants to roll away, and you want to be as precise as possible since the more you have to move the boulder around you increase the risk of damaging the liner.
Safety is the number 1 goal, nobody should get hurt building a pond or a stream. Sometimes you have to take a step back and assess your capabilities and the ones you are hiring. If it is too difficult or dangerous then go to a second option. I certainly did that, at the end of the day no one is going to notice that you used a 24" stone rather than a 30" stone. I had a large boulder that I really wanted to use in my build, but it just became too risky and not worth the effort. Went on to the next stone.
Sorry to give you more to think about, but you may want to really talk to the excavator to discuss the exact boulders you are thinking of moving and exactly where you want them placed.