If you’re afraid your sanding skills aren’t good enough, I’d honestly think about leaving it alone or sending it to a professional, be it the PTC or somebody else cheaper.
Not that I would ever try and talk somebody out of a project but, unless you’re doing it for fun or have a desire to learn how to finish guitars, no matter what you do it’s gonna be expensive. Plus like, you will save exactly zero dollars doing it yourself, and you will kill whatever resale value you’d have left in the guitar body.
Now that the disclaimer is outta the way....
Chemical stripper can stain the wood if you’re not careful, and will lead to a delicate sanding process
The heat gun can burn the wood if you’re not experienced with it, and the scraper you use with it can scratch the wood, leading to another delicate sanding job.
Sanding the poly off is terrifying but, if you’re after just getting rid of the clouding, may be the best option since the clouding occurs between the coats of poly. You could be the luckiest person alive and just take off enough poly to get to the clouding and stop there.
But.... no matter what you do.... there’s gonna be a lot of sanding.
You know, people kinda look at sanding as kind of an “entry level” job at guitar manufacturers, and it is. But not because it’s easy or just because it’s a lot of manual labor that’s “below” more intelligent workers, it’s because it’s literally the most important skill to master if you’re gonna work with guitars.
If you can’t handle or master sanding then, GTFO of the guitar making/fixing world. The folks that sand guitars at PRS are gods in their own right.
So, part one of “what’s the best way to achieve this” is.... sanding. It’s also terrifying.
Be mindful of the dish-edge of the contour of the top, and pay special attention to the raised area around the lower cutaway and horn, it’s super easy to f@ck that up in an instant.
If you don’t own an orbital sander, buy one. Don’t use one of those palm vibrating sanders, it’ll leave lil squiggly marks that are impossible to get out.
And if you buy that orbital sander, leave it in the box until you get to the back of the guitar. The videos of dudes sanding the finish off the contours with an orbital sander in seconds will not be you. Those guys are superheros, it’d be like watching a video of (insert famous sports hero or bukaki porn goddess here) doing what they do, and you being like “oh, that looks easy! I can totes do that!”
Nope. No you most certainly cannot. I’m not saying I’m a better man than you, just trying to keep you from making the same mistakes as I have.
Sorry for the long and rambling post but... your question(s) kind of warrant one. Refinishing a guitar is a long and arduous task, there is no quick and easy solution that’ll make your guitar look un-worse than it already does. If you decide to go at it yourself, I’ll be more than happy to cheer you on and help you out in whatever way I can, even if it’s warning you of mistakes I’ve already made, or putting my arm around you and letting you cry when you burn through your new top coat when polishing it.