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Then go for the option where all the voting happens at one step based on preference. If you still want a best of two you can have the primary election earlier in the year with a score vote tally, and the two candidates that have the highest scores votes from that process then go into a head to head FPTP style for the general election.
For the record both Alaska and Maine are currently using an Alternative Voting system as well as many countries in Europe. Australia also uses an Alternative Voting system. So it can be done successfully in many countries without issue.