Welcome to FT kiwimagic

I presume you're planning to start from TUN because it is one of the cheaper locations from which to start a DONE5.

How to book and pay
As you probably know, using the on-line tool the airline of the first flight does the ticketing (in general - there are a few exceptions). Since your first flight is TUN-LGW, your ticketing airline is BA, which is known to hit you with heavy fuel surcharges. (The on-line tool shows all the various taxes and surcharges - scan through them and you can easily spot the fuel surcharges - they are the big numbers!)

Purchasing by not using the tool usually has the gotcha of you pay the higher of the price of the country of origin or of the country in which you purchase (or you somehow arrange to pay remotely in the country of origin).

However, some good news for you. There is a specific exception for Canada! You pay the fare of the country of origin. (See Rule 15)
So you can just call up the AA RTW Desk, tell the agent you are calling from Canada and set everything up. Since you have an 'over water' AA flight (DFW-SCL), there should be no issue with AA doing the ticketing.

Paper or eTicket
Some prefer paper, some don't. I'm in the don't camp.
Changes to electronic tickets are easily made by phone; paper tickets mean going to an office, or desk at an airport, to make changes
If having difficulties at check-in, a paper ticket is strong evidence of your booking; however you should always have a printout of your eTicket with you.

Four AA Flights
AA does not, currently, enforce this rule.
I acheived PLT status, via the challenge, in just 2 AA flights