you could do both.....dont think you will get a good finish just filling and sanding without the lining paper thats the way i would go...maybe someone else can help....!
if you cant rub it out its quiet possible that it could have been a nail or some sort of metal in the timber when it was alive or a possible deseas in the wood
hi 400 grit is a bit fine use 240 on the existing gloss work it will give u a better key 4 the undercoat to adhere to,then use a 320 before re-glossing......
use a foam radiator roller and dont try to cover in 1 coat,rub down between coats .. 1 primer, 2 undercoats and then a top coat of gloss or betterstill satinwood. the grill is a pain to coat but spraying is the best way..