the hub itself sticks out about 1/4”-1/2” in the middle of the rim
Spacers are the cure for excess length of many things, including any front spindles' axles. If your spindles' axles are an inch too long, you just put an inch of spacers behind the hubs to hold them further out on the spindles' axles. Of course, the further out the weight is on those axles, the more force will be applied trying to bend those axles. When possible, having axles that are short enough to begin with brings the wheels further in, reducing the bending force on the axles.
That said, you can also put spacers on the outside of hubs when the spindles' axle are too long. Don't see it often, but mechanically applying physics it works the same. Whichever way, just be sure you're not using a Chevy hubcap for a spacer. Spacer should only contact the bearings in the hub (on the inside and/or on the outside) so it doesn't need to spin, not the spinning hub itself which would just grind down.
You can order lots of different length spacers of the correct I.D., mix and match them to get the length you want, or do what I do. You can slice any piece of common galvanized or black iron water pipe or nipple from the local hardware store to the length of spacer you need. 3/4" pipe slides right over a 3/4" axle, same for 1" pipe over 1" axle. 5/8" pipe is different in that you can't find it, pipe goes from 1/2" to 3/4". Of course, you can get 1/2" fender washers (oversize) and drill them out to 5/8".
8” on the back would 8” on front mess with the handling/speed of the kart?
Yes. Staggered sizes may look cool, but chances are it would be more stable when all 4 corners have the same size tires. Others may say it's unimportant.