Partly it would depend how far from your camp/car you would expect to down your elk. I carry a bunch of stuff with me too, but I think that is inefficient and unnecessary. In the future I would like to go in with my Bull-Pacs (excuse my spelling if I have mispelled this brand) with my heavy cotton cloth game bags lashed to the frame, my tools (two knives and a Wyoming saw), and my other necessaries (bottled water, clothes, extra cartridges). I would like to be able to make my first walk back to camp carrying a load of elk meat.
With reference to the plastic bags. If you put your elk in a cotton game bag, and then put this cotton game bag inside a plastic bag to keep blood from leaking over you and your pack, I don't see that the elk in the plastic bag would cool any slower than the elk in the cotton bag alone. Heat conducts across a thin layer of plastic. What is of concern is keeping the elk meat wet -- from blood contained by the plastic bag -- which is an ideal breeding ground for bacteria. I would think that if you did not leave the elk in the plastic bag for long -- say for 90 minutes while packing out that portion -- that this should not be a problem.
One thing to remember about bacteria is that it is always present, you aren't going to entirely avoid it. What you want to do, however, is to discourage the rapid reproduction of bacteria -- warm wet conditions. If you can control the bacteria long enough to get your meat frozen, then your meat will be in good condition. No one's meat, however, is truly bacteria free.