Do you have access to electric service, 120 volt AC ? Are you in any kind of hurry ?
Does the thought of doing a section each day appeal to you so that you can
polish the whole thing over a week's time ?
10 in random orbital polisher
If so this would be my suggestion. Harbor Freight sells this polisher for $20 plus tax.
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Shop around to find polishing compound for as cheap a price as you can find it.
Harbor Freight also sells replacement pads for this polisher too. You may want an extra pad or two.
A step ladder may be handy to have while doing this too. Then do a little each day so you don't
burn out or make your muscles too sore.
I've seen people use cheap tooth paste for buffing out plexyglass
boat windshields too. (when they have become clouded just like car
headlight lenses)
Generally when polishing paint you will want a slower tuning turning buffer.
Something like 1200 rpm. This polisher states it can turn up to 3000 rpm.
I've seen people paint whole cars with spray paint cans. Then wait a week or two
before polishing them out. Generally painting them white or black so they can
buy plenty of one dollar spray cans.