I don't know how well it will bind with HDPE, but another easy solution is dissolving packing peanuts (the styrofoam ones, not the starch ones you can eat) in acetone. You will need cups of peanuts for a tablespoon of acetone. It produces a gooey plastic by breaking the polystyrene bonds. This can be smeared over the plastic, and then as the acetone evaporates, it will harden.
I can remember my high school chemistry teacher talking about that he used 50 gallon plastic drums cut in half to provide water for his horses. They had heaters in the winter, and if the water got to low, it would melt a hole in the barrel. This was his preferred patching method. Cheap and really easy.
At the time, I played around with it at home and also found it makes a fun poor-mans napalm that will burn forever.