2mm isn't very wide and the damage looks to below the area were the rings run. My muggy is worse than than, more like 10mm missing and above the exhaust port Cleaned it up with wet & dry on Camlam recommendation and its done around 6k mile since.
Are you sure it is the plating and not piston material which will scrape/emery off? You may be lucky if not too bad as the rings wont reach that level and the little pits won't hurt.
I usually start with coarse emery wrapped along a dowel to take the worst off then onto fine to get rid of the last alloy then a hone . I have also used an emery flap wheel as it would be a long time wearing the plating. As long as the plating isn't flaking around the pits then it should be ok.
buy a new piston,
its hard to tell how bad the barrel is damaged from the pictures.
take the barrel to a good reliable scooter shop or even better a good respected tuner if theres one close to you.
I would just get it plated to be honnest as i dont scimp and save on anything like this.
Im not calling you a bodger or owt but if your in doubt do the job once and do it right.
Just imagine if you just clean the barrel up and the first time out it goes again , the first thing you would think is bollox i wish id had it re plated ,
good look anyway and let us know how you get on
if you are getting a new piston then get it libed for you peace of mind.
if you are getting it relind send it to you know who for some tuning work before hand
has that seized on the cylider stud areas? , was the head torqued or tightened?, what studs you using?