I don't know if I have any better answers regarding gluing of PE, George (@gblair). I have found that for the ladders , for example, that the best thing is to use the super thin glue and let it wick into position, but this creates puddles that need to either be cleaned up or hidden. Paint can sometimes hide these. Clear coats can as well. Using old CA glue definitely has issues with sticking, requiring longer hold times.
If the part being glued to can be placed and held in an unmoving condition, and the part being glued can be placed in a position where it is correct before gluing, AND... you are very careful, you can using a glue applicator to wick the glue into place. But this often results in the part being knocked out of position. So I don't know.
As for holding parts on the bench, something I am going to look into is a piece of foam, or rubber, or perhaps a lint free cloth that I can rest the parts on. It would have to, in turn, be held in position somehow. Perhaps taped down, or as part of some weighted work surface. The idea here of course is that the foam, rubber, or cloth provides a less slippery surface to work on.