Your best bet is to go back and get the right plate tracks for the job. With all that weight on there you don't want to have stuff bouncing around.
A better way to get the wall to stay cool is to build your back wall first and then build a second wall in front of the first. Then leave a 3 inch gap between the two walls and leave a 6 inch space at the bottom and 2 feet at the top.
What this built out wall does is it collects some of the escaping heat and causes a convection of air behind the stove and recirculates this warm air into the room. It also keeps the wall behind it much cooler and you don't end up with any heat damage to the walls. When you use steel studs don't forget they collect the heat and expand, then cool down and start over with the heat again sometimes this can decrease the life of the wall.
As always you need to install the stove the distance from the wall which the manufacturer recommends.
I sort of answered your question, hope this helps.