I have a little paddling experience.
I can't say I took a rifle along.
There is always a little water in the bottom of the canoe.It drips off the paddle when you switch.A little water climbs in the boat once in a while.I recommend a large sponge .
But you do not want your rifle laying in the bilge.
I suggest you rethink"easiy accessable".IMO,your rifle should be secured to thwarts or up under a seat.I like the 1 in wide cam lock straps available from outfits like NRS.Your canoe or a rental?If it is yours,you can outfit it with attaching points.If it is a rental,assume you will only have the thwarts.
If you have a secure,strapped in, set of waterproof river bags strapped into the canoe,midship,low,you could attach rifle rifle over the top of those.
It is nice if you can stay upright and dry.Pack with the assumption you will dump it.You do not want to hunt down scattered sinking stuff.You do not want to lose essential gear in the bush.
Also realize there are few places in acanoe you can put a long gun without the muzzle being pointed at someone.Be very conscious of keeping the rifle unloaded.
I suggest you just lose the idea of shooting from the canoe. The greatest tool you have for keeping your canoe stable...and upright,is your paddle.You need two hands on it.The paddle on the water is like a walking staff.If you are determined to hunt from the boat,bow man only with the rifle
I suggest,travel backpacker light,plus just a little comfort.Not much.A canoe is not a pickup truck.Every pound you leave behind is a pound of buoyancy.Your boat will float higher,respond better,be faster if it is lightly loaded.All the gear must be repacked every day,and,consider the portage.Do not be the guy with 6 trash bags full of WalMart inventory laced in with 300 ft of paracord and 79 knots.(No,I don't want to talk about how I know that!)
I put together my river outfit,based on two waterfroof river bags.Tent,thermarest,sleeping bag fit in a 1.2 cu ft Bill's bag.Everything else went in a 2.2 cu ft Bill's bag.3.4 cu ft would be a monstrous backpack.
Also a day pack for the small accessable stuff,and some water.A gallon water jug is great for fine tuning trim.Look at the water on the bilge.Use it like a bubble level.
I suggest you beach and secure your boat(always tie it to something)then get your rifle out.
NRS or Bills bags does sell a long,skinny dry bag for tents,etc.It might work.
And,they sell raft repair material and glue.You could use those to make your own dry bag for your rifle.Myself,I think a Kolpin hard case in a canoe would be cumbersome.
IMO,there is a lot to be said for fishing and taking pictures.For a deer....44 mag handgun is more suited to a canoe.It would handle a black bear problem.
Moose ?Well,OK.But,IMO,a classic Bubba'd Milsurp carbine ,like an 20 in bbl Yugo mauser in 8mm loaded warm with heavy Noslers is a canoe rifle.Or a Mosin.A battle rifle that can get wet and beat up,yet hit at 100 yds Then,don't worry.Be happy.Wipe it off and oil it every night.Fastex strap it muzzle forward to the bow seat.You could have a little rope loop off the bow "deck plate" to poke the muzzle in..Then its strapped in,secure.Wrap it in something waterproof,like cheap grey tarp if you like,cut to size.A stocking foot hip wader? Red ball makes them.Leave the weatherby at home.