Rear track width

I have a question concerning rear track width. My current rear track width is 46.5 inches (center of rear tire to center of rear tire) to fit a custom nostalgia altered body I did not want to cut up. As we get faster (7.0 et range) the handling of the car gets worse. I can easily narrow the track width to 40 inches but will have to change bodies.

Should the 6.5-inch change in track width improve the cars handling (looking to run in 6.8et range) or is the change not enough to notice an improvement and I should look at some other option.

Thanks in advance for any advice.