Hello,
You are right, either +1 or 001 would work in this case. However, using the plus sign isn’t possible with any phone. Mostly cell phones allow using + and still, the “official” way to dial internationally is by using an IDD code (00 for Europe, 011 for the US and Canada and so on).
One question: do you find our dialing instructions confusing? If so please explain, I always appreciate criticism.
Thank you.