The width of a slick is measured across the tread. The width of a DOT tire such as an ET Street is measured across the section width. Using MT tires for sizes...
Your 28x12.5 ET street has a 10" tread and a section width of 12.6"
A 28x9 slick has a tread width of 8.5" and a section width of 11"
A 28x10.5 slick has 10" tread and 11.7" section width. This would be very close to your ET street tires.
A 28x10.5W has 10.9" tread and 13.1" section width. Depending how close your ET Street tires are, this may be the limits to what you could use without doing sheetmetal work.
I was able to squeeze a 29.5 x 10.5 slick under my fenders but it requires a bunch of inner fender modifications to allow the taller tire to fit under the fenders. My car is now back halved and I run a 32x14 slick
If you want a DOT tire, you can easily use the MT web site to see the dimensions of the different tires. Since you know how much clearance you have around the 28x12.5's, you can get a rough idea how much more you can go. Going much wider than that and you may need wider rims. The narrower tires work well with an 8" rim but going to a 10"+ wide tread should use a 10" wide rim. You never stated current rim size or backspacing.
