I'm gonna have to be honest on this. Personally, I don't think we should HAVE to face gym #1 first because #1 could be harder than say, #8. It's not an incline of difficulty, but an incline of the number. I know it's supposedly designed to be like D/P, but I don't think in this situation that it would be possible. Here's ABY's suggestion.
1. A challenger comes! He/she wants to battle and get a few badges with an amazing team.
2. Any gym leaders on at the moment lay out their acceptance of a challenge. The fights begin! Given a number of chances per day, the challenger fights and fights the gym leader up to that may times per day.
3. The challenger goes happy or sad with their badges or without them. This way, challengers can actually have a chance for badges. Those who haven't shown up for at least 3 days to check up on the thread may be removed if there's a replacement at hand.
That's all I can think of to keep a good flow of challengers up and moving and getting some fights in. Those holding all 8 badges may face the E4 then, with proof of the badges at hand (in the sig to say). With each E4 beaten, then that person, is indeed, the champion.