If carbon does absorbs ammonia then I'm not aware of it.
Yes, you're right regarding everybody has different opinions.
Definately clean your gravel!!!!!! Any excess food / waste will have worked its way beneath your gravel substrate and will be rotting which causes ammonia, this may be the reason for your little spike of ammonia you are now experiencing. I recommend you do a good deep gravel vac and large water change and keep your eye on your stats again, you may find they stay at zero then and the cycle could be complete.
Regarding the filter media, you could replace the carbon a bit at a time. Cut about a third of the carbon pad off with scissors and replace it with a third of new filter sponge. Do this each week, a third at a time so after 3 weeks the full sponge should have been repleced.
Andy