With only 3 coats of clear and having already sanded it with 800, you will want to be very careful not to remove too much clear during your cut and buff.

Since it sounds like you don't have the place or the tools to apply more clear then I would proceed carefully.

In places where the scratches are obvious you will want to start removing them by wet sanding with say 1200 grit. I would apply a black dry guide coat prior to wet sanding as it will help you see imperfections that need attention without sanding too much clear in other areas.

Here's a picture of my GTX hood where I used guide coat during the cut and buff process:


When you get the 800 scratches out, move to the 1500 grit to remove the 1200 scratches.
At this point, I would try a twisted wool pad on a rotary buffer and some Meguiars M100 compound. Again working a small area at a time and I think you will see an great improvement.

If not then wet sand with 2000 and then buff it.