The buzzing sound could well be the new gears meshing as they turn. I'm going to assume they are plastic?
Recently I've replaced the top gear on the vertical shaft of two Singer 413s and found they rattle and tinkle, and clatter from the bobbin area no matter what I do. But then so do the 338, and the 518.
If you have the timing set right, and don't have the "fit" of the gears and shafts too tight, I'd suggest putting some Tri-Flow grease on the plastic gears. The factories put some sort of grease on them, I've seen that a lot. So since I don't have their grease I use the Tri-Flow.
Then just use the machine. All of ours seem to be noisy, I think it's their nature.
Joe