I do get where you're coming from re. the solution.
The parameters of the puzzle were unclear, so I sought clarification, and this cause you to accuse me of over-complicating things.
When I got down to 13 players, I thought 'Ah, I bet this is puzzle is about finding a clever solution when you have an odd number of players in a round'. But I couldn't find one, so I asked for clarification.
You're entitled to your opinion - and you're also entitled to run a tournament where some players get an arguably unfair advantage due to a bye - but I maintain that I wasn't over-complicating things.

Jeff