I have a 20” Horizon with their convection plate. 50 degree differential from firebox to stack side at grate level is pretty common. It will even out at the lid thermometer more - I get around 5 degree difference on the lid.
Also, the convection plate has a lot of thermal mass and holds a good amount of heat. If it’s close to the grate, that thermal heat will increase the grate temps over it. It will cook from below like a reverse flow does. I cook without mine most of the time as I don’t want the radiant heat.
Small smokers with small fire boxes are a challenge to even out the temperatures on.
Also, when you mention having problems with stable temps - are you trying to hold 250-275 burning sticks? Usually you cook in a range that is wider than that on a stick burner (small ones at least).
I aim for 275. I throw a split or two on when it drops to around 250. It spikes up to around 300. Settles in in the general vicinity of 275 for bit, then starts to drop.