Lee copies stuff from other sources. He rarely reference the source. The 62 FMJ is not listed on most manuals as it is a weight that is kind of odd to be seen in the fields. Most 223's in that range are 60's an65's and 69's. Because LEE does no work on his own I have never bothered to pick up one of his books. Lots of guys love them and they work well for them. I prefer stuff from the bullet and powder companies. I think I use books from six different companies and the variance from book to book is very educational. On that note I will point out that manuals are GUIDES and are not carved in stone . Any time you step away from any published spec as in bullet, lot number of powder or primers and barrel manufacturer you have just turned the book you bought into a suggested not a mandatory tome. Just like buying a cake mix we all add or subtract somewhere on that recipe.
The pressures will not get out of hand seating to the canneleur Internal pressures will go up but realize that seating deeper also raised the volume of the chamber thereby increasing burning area and lowering the pressure. It's a teeter totter on pressure. If you seat way away from the lands, and 2.22 is not that far, you will increase internal case pressure. As you lengthen out the case pressure drops. As you get longer the distance to the lands will decrease causing a rise in pressure as the bullet is now starting to engrave and pressures rise. Think of an inverted bell curve for pressure with uber-short to the left and uber-long to the right. I just ran a load using a 68 grain Hornady match bullet as they did not list the 62. The pressure difference between 2.220 and 2.260 ON THAT bullet was 1,428 PSI. Both were well below the 55,000 you are dealing with. This is a COMPUTER MODEL that will get me close in most cases but not something that a guy will bet the house on. Range numbers and observation need to be applied to it.
The COL on handguns cause more issue as their capacity is so low that a 0.050 shortening can raise pressures as opposed to a rifle cartridge where you may see a slight increase but well within the safe operational MAX. You will find that MAX on any non-target application 223 will never exceed 2.260 as that is the internal size of the magazine we feed through. Seeing one that says 2.350, many do BTW, means you are dealing with single load long range stuff or altered mags in the AR. Many bolt guns can handle the extra length. We have 223 AR mags from ASC that are STAINLEES STEEL that will allow us to laod out to nominal 2.316 and these are a boon for getting close to the lands. Most AR's won't ever get you close on the lands on a factory barrel. I shoot custom barrels with custom reamers and my specs are designed around shooting a family of bullets that will actually let me go to or in to the lands. A bit more esoteric but still embodies the realm of sane pressures and gear management.
Good luck on your work. BTW I don't crimp any AR loads relying on resident neck tension to handle the job. Many disagree but my side of the argument has lots of support. My trophy rack is anecdotal proof of it too..LOL Loading for a bot gun vs an auto does have some nuances when it comes to tolerances. Chambers difference may enter in to it but as long as you run 0.003-0.004 tension you will be home free onthe 223 AR. In bolt guns I will go down to around 0.0005 to 0.002 depending on the cartridge and usage.
PS: One last safety tip on the AR. NEVER NECK SIZE ONLY!!