Could you possibly get the other carb on it & see if it runs w/ the stocker on?

I'm assuming you have some experience or you wouldn't be putting a savage in a gs frame.  But why did you let a shop replace the cam chain?  The uncertainty factor here is did they get it timed right?

It's not unusual for the carb to spit at idle, been asked about many times, seen it myself.  Generally asked about when there's a fuel problem.  so try it on prime.

Ok, so trying the stock carb is a good idea, and understand it won't fit in the frame.  Take a look at lancer's Rex.  He side mounted an edelbrock and routed it with black plastic pipe from homedepot or the like.  so something similar can be done with the stock carb.  Even if you ran it straight back it be ok to try.

when my carb spits its because i forgot to turn the fuel on with the raptor petcock  so theres only a little bit of fuel in there

No guesswork in pulling the head cover. Might not be possible in that frame, IDK. There's a cam timing diagram , page 3-29, Suzuki manual. Exhaust opens 64 degrees before bottom dead center, at the end of the power stroke & closes 14 degrees after TDC, as its getting ready to start the intake stroke. Intake opens 22 degrees before TDC & closes 59 degrees after Bottom Dead Center, as it gets ready to make the compression stroke. So, if you can get a degree wheel on the end of the crank, you can check the valve operation against the way theyre supposed to work. No guesswork in pulling the head cover, but IDK if thats possible in that frame. I hope the mechanic used a THIN film of goo for a gasket on the head cover, since that sets the clearances for the cam & a loose fit will screw things up.

Id be knowing the cam timing is off before I walked away from it, expecting him to open it up & see its off & take it in the shorts.