I was under the impression muscles grow more when pushed close to failure, so why wouldn't you want to do that in the low weight/high rep sets?

Responding to this specifically - this generally seems to be true according to research for hypertrophy, but it's worth noting that GZCLP is a powerlifting program, not a bodybuilding program, so the emphasis is on strength, not size. The T2s are there to support your strength on the T1 movements. If you want to build size too you can treat GZCLP like a "powerbuilding" program by pushing the T3 movements, which are more appropriate for hypertrophy work.

Also, if you haven't it's worth reading Cody's original posts on the GZCL method for more of the context. He even addresses your specific question, where he says AMRAPs are okay on T2s but to use caution:

Options to push T2 effort during the cycle would be to include AMRAP sets, as shown with the Week 4 example, or limit rest. Be aware that over use of T2 AMRAPS is likely to cause a decline in T1 ability later that week if recovery is an issue. This is especially true if the T1 is also utilizing AMRAP sets.

Tier 2 sets are there to build volume and practice for those lifts - more reps at a lighter weight. I think you can definitely make your last Tier 2 set AMRAP as long as you can still finish the accessories. The order of exercises doesn’t really matter, personally I would try to do the Tier 1 sets first so you can get your maximum effort on those heavy sets, but the main thing is to complete all the sets