I do not think the bolt swap is a drag and drop procedure as you need to account for headspace and I am not sure the USGI bolts are always compatible with the chinese barrels. That is why everyone recommends to take them to a good M14 smith.
It is NOT a DIY project. You need to have someone who is a gunsmith and who knows what they're doing, particularly with Chinese M14s, do the work for you.
Basically, there are three "big names" in converting Chinese rifles to handle USGI bolts; Fulton, Smith, and Warbird.
Fulton is the most expensive of the three, and they will insist that you scrap the chinese barrel and have them install one of their own. While I don't think anyone will argue that their work is shoddy, there are many who will argue that you don't need to scrap the chinese barrel. Fulton is, I believe, the most expensive of the three.
Second is Smith/SEI. I know very little about them, except that their work is top notch, they are backordered to high heaven (last I checked), and they ain't cheap, either. I don't know if they require you to scrap the chinese barrel.
Warbirds is the smallest operation of the three (it's really just one guy), but he has a great reputation. He will NOT require you to scrap the chinese barrel, he will mate the USGI bolt to the existing barrel. So far as I can tell, he's very reasonably priced. I'm about to send a rifle to him for this very same type of work. I can't think of a better endorsement.
Here's the slight longer version of why Polytechs are so good, and why you need to have the bolt conversion done, or at the very least watch your headspace carefully:
The Polytech reciever as built around M14 match-grade receiver blueprints, and the chinese made it out of extraordinarily good steel. The rest of the gun, though, they reverse-engineered from M14s and M1As they obtained through various means. This includes the bolt. The bolt is not dimensionally correct in most examples and the lugs are not hard enough in many of them. This results in the locking lugs (the things protecting your face from the contained forces of the 7.62 NATO round) not always mating up properly, and they're frequently too soft. What will happen is that they will start to deform, due to all of that pressure being borne on a smaller area than planned, and that smaller area not being as hard as it should be. Eventually, the bolt will start to not return home and lock up in the right place ("right place" being measured in thousandths of an inch, you can't eyeball it), and your headspace starts to get larger. Soon enough, the headspace will be excessive enough that the thing can Kaboom.
This does not happen on all Polytech M14S guns. Some of the bolts are hard enough to handle the stress. Some of the bolts mate up a little better with the receiver. Some guns aren't shot enough. AFAIK, there's no way to tell until you start to see deformation, test and see excessive headspace, or the thing s'plodes on you.
This may seem bad, but it's not. As was mentioned, the receiver is EXCELLENT. You have the basis of a
very good M14 in your hands. Swap out the bolt, have Warbird or someone else match it to the receiver and barrel, and you will have an M14 that is built on a forced, dimensionally correct, tool-steel reciever, with a very good chrome-lined barrel (there's nothing bad about the barrel) and a USGI bolt. That will be a very good M14 clone that should outlive you, even if you shoot it alot. And, it will cost you way less than a new SAI, and will be a more durable gun.
AFAIK, the reason that some gunsmiths say you need to replace the barrel is ostensibly because the USGI bolt will not match up right with the chinese barrel extension. Some fiddling little work will need to be done to the bolt and the barrel to get it mated right with proper headspace. Rather than take the time and effort to do that, they'll offer to remove your chinese barrel and replace it with one of theirs, for which you must pay. Pessimists will say that there is a profit motive there. Others will say that it is because mating the two is tricky and may not work right. Tim at Warbird is very outspoken that he can and will do it properly, can and has done thousands properly, and that you don't need to scrap the perfectly good (and chrome-lined!) chinese barrel. I don't know who is right. I'm not a gunsmith. All I know is Warbird's work is good and his rifles shoot fine, with the Chicom barrels.
If you opt not to have the work done, or decide to do it, but put it off, do yourself a favor. Get headspace gauges and check the rifle every time you go shooting. If you start to see changes, STOP SHOOTING AND GET THE BOLT CONVERSION DONE. Once they start to go, they go fast. Certainly if the bolt closes on a field gauge, you have a grenade on your hands. You can also strip the rifle and look for signs of peening and deformation on the lugs. If you see any, STOP SHOOTING IT.
We wouldn't be warning you if it wasn't a serious issue.
Mike