I have never hunted Clinton (camped and fished there a few years ago), but I hunt public land in the northern part of the state a lot. You have the right general ideas about public land -- the farther you can get away from others, generally, the better you will do. (Have a plan on how to get an animal out). If I recall, Clinton is long and narrow, spread out along the lake, with lots of parking lots, so it may be difficult to get away from people (you'd know better than I though, I suspect). It's not realistic to plan on avoiding everyone. You will bump into people from time to time no matter what you do, but most people are decent, in my experience. If you want to gun hunt, you don't have to give up on this year. There are a few permits left (there's a list on the IDNR website), and most sites allow walk-ons (for whatever reason, some people don't show up, and they lottery off the remaining tags for $5 per day). Talk to people in your area, there are surely some sites that are easier to walk on to. Also, on public land, have plenty of back up plans, someone may beat you to your spot.
Good Luck.