Try getting a BGA jig like this one
Avoid the other types as most are not suitable for the switch SoC as the jaws are too low which means the stencil has too much height and the balls will roll around underneath. they also don’t grab the IC all that well.
and then a dedicated 90x90 stencil such as this
As @Solac03 mentions, you’d remove the stencil after filling the balls and then remove the IC from the jig, then reflow the balls.
Alternatively, you can just use the stencil you currently have with the preformed 0.35mm balls, and you can leave the stencil in place and directly heat and reflow the balls in situe, you don’t have to remove the stencil prior, it will still likely buckle when you apply heat as it has done while your using solder paste but unlike solder paste, this doesn’t have the same negative effects as, wheras the paste will try to run and merge together below the stencil with the preformed balls won’t
The only issue with this aproach is it will be messy and you’ll have a hard time getting the balls into the stencil without the bronze jig above, as you can’t swirl them around.