It's nice to see someone else tackling the paint problems. Let us know how it worked out as I have been afraid to re-clear coat one spot on my headlight pod.
A few years ago I finally attacked the car with a full program of wet sanding and polishing. By using a succession of 1500, 1700 and 2000 grit papers (all with a bit of dish washing liquid in the water to keep the paper from gumming up) I was able to get rid of most of the orange peel. In a few areas I was afraid to keep sanding as it seemed that I was taking quite a bit of clear off the car so I didn’t remove all the orange peel. I then worked through various levels of polishing compound and ended up with a nice shine.
What I learned was: 1) Plan on spending a great deal of time. 2) Wash - Wash – Clay – Wash the car before starting with the compounding or sanding. 3) Wash the car immediately before any sanding or polishing or when changing product. If there is any road or atmospheric grit on the finish when you start sanding or polishing will be ground into the finish. 4) Start at the least aggressive method and then go to a more aggressive method if the first doesn’t do the job. Because of this I spend about three days doing the driver side door because I started off with a fine polish working my way step by step learning what each polish or paper would do before ended up with 1500 grit wet/dry paper as my most aggressive method. After this bit of leaning thing went more quickly although the drivers side door is still the nicest panel on the car. 5) Stick with one brand of polishing compound. That way you can easily get a good idea of what the differences there are between the various levels of aggression (girts). 6) A good orbital sander with foam waffle pads gets results a great deal faster than by hand. 7) Ease up around edges. I have light scratching around the antenna because I was too heavy handed.

Park on a plastic tarp. Having a nice clean place to put down your tools keeps grit from getting on thing and ruining your work. 9) Don’t skimp on supplies. Having plenty of waffle pads, sandpaper, towels makes things go more quickly and keeps you from cutting corners. Remember to mark each polishing pad so you don’t use a pad contaminated with aggressive product late in the process. 10) Always use a rubber backing pad when sanding. It distributes pressure more evenly than your hand can. 11) Do one panel at a time. It helps you see and compare the results. 12) Finish the process with clay. If you feel the clay doing anything it means that you have not done the polishing correctly. It acts as a final quality check.
I am sure I learned and forgot more about the process but that will have to wait until another time.