The main jet is not what operates when the throttle is closed.  With a closed throttle the slide is completely down, the needle is dropped down into the needle jet, and there is very little fuel coming from that circuit.

During deceleration the only fuel supply is through the Pilot Jet....and through the TEV valve (if it is functioning).  The TEV valve diaphragms get stiff and they may no longer be working as they should.

A 52.5 pilot is likely as big as you need.....you can determine that by adjusting your fuel mixture screw.  Get the bike fully warmed up, back the idle speed down to around 800 rpm, and adjust the fuel mixture screw for the best idle.  If you can turn the screw all the way in and the engine is still running.....your pilot jet is likely too big.  If you have to turn the mixture screw out more than 2.5 turns....the pilot jet is too small.  The proper pilot jet size allows the engine to run smooth with the screw between 1.5 - 2.5 turns out.  When done be sure to turn your idle speed back up.  (Don't let the bike lean over on the sidestand while doing this adjustment - either straddle the bike and hold it upright or put a block under the kickstand.....idling on the sidestand starves the right side cam bearing and exhaust rocker for oil).

You should not be jetting your carb for how it runs with a closed throttle......you should be jetting for how it runs when the throttle is being opened or is fully opened.

You can reduce the backfiring by not allowing the throttle to close completely while shifting gears or decelerating.  You don't need to use a lot of throttle....just enough to stop the noise.  After you do this for a while it will become instinct and you won't even notice it.  You might even try leaving the choke out 1 notch in cold weather.....the choke works on the pilot circuit and only works when the throttle is closed (if you hear the bike running rich at idle then push the choke off).

Turning your idle speed up a bit can help as well - maybe you only need to do this during cold weather.  The Savage has a adjustment that can be turned with your fingers.....adjusting it to suit the weather that day is acceptable behavior (you will be acting like the computer on a fuel injected engine to make the necessary adjustments).

I live and ride at elevations between 50 - 800' msl.  My "go to" jetting for setting up a carb is a #50 pilot, #150 main and replacing the white spacer with 3 machine screw washers.  Sometimes the bike would rather have a #52.5 pilot.......sometimes a #147.5 main is better.....and I have had 1 bike that had a lean surge at part throttle with 3 washers and it ran much better with just 2.  If you bike is jetted well you will notice it being just a bit cold blooded and

Check the exhaust. Make sure you are snugged down. It'll bang like a gun if it's loose.
Don't try to get them tight enough that you won't have to do it again. Strip the threads or twist off a pukey little bolt in such a place to get lined up on it and you will cuss yourself.