If you have a non restricted barrel and a complete restricted rifle all you need to do is remove the gas system from your factory barrel and install it on the new barrel then take it to a firearms verifier for inspection and complete the paperwork. Once that is done you sit back and wait for the CFO to complete the reclassification. You need to call them regularly because they won't notify you when it's done, it will just stop showing up as a restricted firearm once it goes through.
Just remember that even though you have a non restricted barrel on it you still have a restricted firearm until the CFO completes their end. Mine took 3 months for them to complete.
Don't worry about stealing the gas system from your 16 inch barrel, you can't legally put it back on the rifle and use it unless you have the rifle classified as restricted again first. If you do you are in possession of an unregistered restricted firearm which could get you some serious criminal charges and potentially the loss of your PAL, your firearms and jail time (that's worst case scenario) so don't risk it.
Cost is approximately whatever one hour labor the verifier you find charges.
Unfortunately there isn't much of a market for the factory 16 inch barrel because even though it will mount into an AR upper it needs to be modified to work correctly. I put my old 16 inch into an AR but had to open the gas port in order to get it to cycle. The nitriding surface hardens the bore to even harder than chrome lining so it's very hard to drill through.