Pglasgow
I have never handled an Apex so I can not really be of much help here. I will tell you have bedded a lot of guns and one of the biggest challenges I had was with a Firebolt - probably a distant cousin of the Apex. In the case of the Firebolt the stock was so flexible especially out on the forearm it did complicate the whole works a bit.
In your description it does not sould like you intend to remove any material from the current barrel channel... So I am not sure shimming the barrel is as lifting the action out of the current seat in the stock, which in turn will lift the barrel.
I bed thereciever first but for me that is a two step process. (1) The first step is to shim the recoil lug(s) up with a very small round piece of teflon at the bottom of the lug - I think the Apex only has one lug. That same thickness of teflon will them be put under the reciever in another spot to give uniform lift - it you have two lugs then the problem is solved. I also drill four small holes at and angle in the bottom corner of eachlug pocket so that glass will be forced into those channels also. (2) after thelugs are set then I set the sides and bottom of the reciever with glass. This process should give you a really solid reciever - then move to bedding the barrel, but I am not sure I would bed the barrel, and again I am only looking at pastexperiances with BPI stocks they are just to flexible. i would really get that action settight and well the barrel floating and then shoot it see what you have... you might be surprised.
I do agree that if you plan to shootthe gun alot you will eventually need to bed the action as the stock is to soft to last forever, but if you are an occasional shooter - it might work just fine the way it is for years.
I use Acraglass as my beeding agent it come in two different forms... a gel (doesn't move at all when you put it in place) and liquid glass (they call it liquid but it is more like heavy heavy gear oil) the liguid will flow and self level. The kits come with a release aget that reall works well. I aluse saran wrap as an isolater on parts that do not have screws poking through/ Saran wrap reall works well under the barrel and even parts of the reciever. make sure that no bedding materail can getinto any screw holes or gaps that could lock the whole system in the stock - doing bits at a time is sometimes better than one job one shot.
Good luck bedding is fun but do it carefully - there should be know hurry..
mike
PS - I hope I have not confused the issue - talking is always easier and less risky than the doing...