Are you sure it's not leaking air in from the connections? To reduce the fitting put a nail the diameter you want and just pinch it down with pliers, solder the seam or not.
Is the tip a size you can get a copper cap for it? If so you could put a cap on it, drill a hole in the cap and test until you get the hole too large. Then put on a new cap and drill in the last size hole that worked.
You could solder a smaller copper tube, about 1/2’ long, inside the opening of the last reducer. Like a sleeve lining. This will create a longer hole than just drilling a hole in a new cap, which I think would help with the surface tension issue. If that new tubing hole is to small, it can be drilled out to something inbetween the original and new size.