You can definitely use a biathlon sling in conjunction with a backpack but it is rather cumbersome to take off/on/off/on/off/on during a match, especially under the stress of time. Lots of straps to deal with etc. That's why I asked if you need to stop at different stations along the way, shoot targets, then move on to the next station and repeat multiple times over the 2 miles. Also asked if the COF is timed. If so, efficient management of gear is important.
I assume the targets are UKD if you are carrying a range finder? You mention shooting sticks and are carrying a tripod. Either is OK per the match rules? Sticks are lighter and more handy to carry/use but a tripod with cradle is more stable.
Sorry, not trying to bust your balls with all these questions. I've just seen lots of shooters come to their first match with extra, unnecessary gear and struggle to manage it making the entire experience unpleasant. Remember, the mission (in this case, the match) drives the gear. Don't bring anything extra you don't need.
Based on what you've said about the match, I'd carry my rifle on a sturdy sling (not a biathlon sling) and put my gear in a small backpack. A 20lb rifle is not all that difficult to carry if you have a good sling. Attach your rear bag to your belt with something like a carabiner. Likewise carry your rangefinder and magazines in pouches on your belt. That way, when you get to your shooting positions, you can unsling your rifle and grab the gear you need off your belt without having to take your backpack off.
When you get to the shooting stick station, you can take off your backpack, retrieve your sticks/tripod and shoot. Put your backpack in your lap to stabilize your position.
Whatever you do, practice with all your gear before the match. Believe me, I've learned all this the hard way

Good luck!