I hate to tell you this, but unless they're ET Street "Radials", you're likely to experience even more instability than before.
The ET Streets are a bias ply tire and don't have the radial case for stability like the ET Street Radials do. The fact that you've increased the sidewall on them now by going from a 17" tire, to a 15" tire may make things worse because you’re increasing their ability to move laterally by 2-inches.
Truth be told, if you’re set on running a bias ply out back, it's your front tires that are causing all that "drift" when you're going down the track. The rear wheels walk around, while your radial tires up front stay planted, which makes them a handful when you're at speed. What you need to do is get a set of bias ply's or skinnies up front that'll work with the bias ply's you have out back. This way, the whole vehicle moves in one direction, or another and corrections can be made easier than they could if just the back end was dancing around. Either that, or re-sell these ET Streets (you could probably make a few bucks) and get yourself a set of ET Street Radials that don’t suffer from this problem going down the track.